Is it possible for a country to be economic & technological super power but to have relatively little political clout?
If its possible under what circumstances it could happen?
While there are already some good answers, it should be noted that for exampled Germany, South Korea and Japan are not economic superpowers, but mere great powers. (Germany and Japan lost political power for historical reasons and held back)
I think a better example could be the European Union.
Imperial China was similar, the political weakness here stemmed from its isolationism. Also, the pre-WWI United States.
An ineffective/non-existent central government and/or a policy of isolationism will severely limit political power while not impeding economic power too much.
It should be noted that the situation is unstable. At some point the political power will be there because isolationism ends or the state centralizes. Or the economic power goes away / the power breaks up into constituents.
Napoleon Bonaparte is supposed to have said “Let China sleep, for when she wakes she will shake the world.”
Known for years as the sleeping tiger, we've recently seen China take a more active role on the world political stage. The words of Bonaparte show that China has had the potential to exert its power on the world for some considerable time, however they have only now chosen to do so.
The key is that, given the economic power of the country, they have to choose to use (or not) the political power available to them. It's innately there as the definition of economic super power means the economies of other nations are dependent on theirs.
The example for the first bullet point is Germany, until very recently. The example for the second bullet point is China, again until very recently. So one might argue that the examples are not stable situations, merely a transition period until the superpower got used to being a superpower.
It depends on how you define superpower, too. During the Cold War there were two, the USA and the USSR. Something that large simply can't refrain from entering power politics. Anything they do or fail to do matters. Compare Japan or Germany in the 80s, or China or India in the 00s. Not quite on the level of the United States, and lacking global power projection, but certainly a major economic power.
In my mind's eye, I could imagine a country which built itself up to be a great economic and political superpower, and then had a leadership change, and due to either isolationism, buffoonery or inexperience (say: inexperience in an at-will market economy), squandered the political power they carried in the world. All the other nations still bought their stuff, it's pretty good stuff, but when they were the one country to back out of a treaty all the rest signed, the rest of the world just soldiered on without them.
You see things like this even in our time. Look at Russia after the Soviet Union fell apart. Still the go-to country if you want to put a man in space, or want decent military hardware a child could maintain.
What makes a superpower "super" is the unchallenged ability to project all forms of power, be able to push past almost all forms of opposition by individual states or even coalitions and enforce their will.
So you can be an economic and technological power, but without the ability to project your power ("Hard Power"), then most of your power is potential rather than actual. The vast majority of examples (pre WWI United States, China up until @ 2000, post war Germany and Japan) lacked the ability to project their power, so even a relative pipsqueak power could simply impose trade restrictions and other means to thwart the will of these relative giants. On the other hand, even super powers know how to leverage their assets. The British, since the time of Queen Elizabeth 1 have preferred to leverage their hard sea power and economic power by providing money and diplomatic influence to counterbalance would be hegemons in Europe. The United States "pays" for a globe spanning navy by using it to enforce free passage across oceans, immensely benefiting trading nations around the world and (through trade) immensely benefitting America herself.
While it's generally true that political power grows out of the barrel of a gun, it's not like guns grow out of thin air either. In an industrial world it is usually it is the more economically potent that can amass the resources to build the military infrastructure and political network to further their influence in the world.
There are however several exceptions to this rule, as in our modern world there are countries that have had their military ambitions crushed in world wars and have for a long time been effectively protectorates (in all but name) of one superpower or another. Germany and Japan have long been quiescent on the world stage, generally preferring to stay in the shadow of the superpower.
Such a situation is however unlikely to persist for long, and indeed we see that in recent decades, both powers have shifted towards a more self-assertive military and political stature.
So to answer the question: yes, but such a situation is generally unlikely to persist, especially outside of a exteremely polarized 2 superpower world context.
Look at ancient Greece and Rome. Before they were conquered, Greece was more economically and technologically advanced, but probably because of their city-state structure and everything that derived from it they weren't really in a great position to push anything politically compared to Rome, Egypt, Carthage, or the Eastern Empires.
Japan and Germany both were limited by culture and treaties after WWII that prevented a military build up(different from political power, but related).
Switzerland has a habit of being politically neutral to the point of it almost becoming an idiom. There are a lot of reasons for this, and certainly you could argue that Switzerland still has a lot of political clout despite this, but they do have to walk a very careful line to not anger or antagonize more militaristic countries around them. https://en.wikipedia.org/wiki/Neutral_country
I would say Pre-WWII United States. Its foreign policy was largely neutral with regards to European powers, with its only aggressive stance was against those that tried to meddle in in the Continental Americas and was content to be a more regional power. I would say that the two things America has in common with Switzerland is that it has terrain features that make foreign invasion near impossible (trans oceanic invasions are still quite difficult without a land based foothold) and the fact that it has an armed civilian population that can be quickly mustered (one male in every household in Switzerland is required to own a gun where as US law will vary from state to state, but no part of the U.S. can out and out ban gun ownership). This makes both countries notoriously difficult to invade and be bullied by people who might have a military advantage. In addition, America loves asymmetrical warfare, which is basically, never engage the enemy in a fair fight. Going to the invasion strategy, the colonies mostly engaged the superior British Empire in guerilla tactics, rather than head on confrontations. As Admiral Yamamoto is reported to have said "You cannot invade the mainland United States. There would be a rifle behind every blade of grass."
Industrially and technologically, America was quite ahead of its time during this period and a major economic player. In both World Wars and the Civil War, failure to claim victory before the United States shifted to a war time economy was a decisive factor in the war's outcome (in the case of WWII, the shift was faster than anyone anticipated. Again, Yamamoto believed Pearl Harbor would buy him Six Months of Unchallenged Navel Power before the United States could muster some defense... and in six months, it had all but neutralized the bulk of the Imperial Navy's threat. In the case of the Civil War, the Confederate States were beaten before the United States is believed to have truly mobilized).
Obviously today the United States has considerable political clout, but it's necessary how one could achieve that. First, the United States sells a lot of weapons to other countries. This has several benefits... first, it's easy intelligence. You don't need to go and figure out a nations military capability when you have the order form for their guns. Second, it's going to have some compliance from most purchasers (you never hear of the gun store getting robbed for good reason). Finally, it removes resources from that country cause fighter jets are not cheap.
Now, that's more economic power than political, but it allows political power to be wielded. Switzerland on the other hand, has put its neutrality to political power by being the country that is neutral. Whatever international organization needs a meeting place will go to Switzerland. Switzerland also will negotiate as the middle man (Any time a US citizen gets arrested in North Korea or Iran, it's the Swiss who do the negotiations, since the US has no diplomatic channels to push its own interests in those countries). It's also very well known for its banking laws and thus, a perfect place to keep the rest of the worlds money safe. Just as nobody robs a gun store, nobody robs their own bank.
So... TR;DR some things to consider:
The two areas where this isn't true are Cuba and Russia. The latter's borders only exist in a part of the world that is not worth an invasion force (Eastern Russian and Alaska aren't extremely populous places nor are particularly hospitable... both sides of that conflict are better allowing the invasion to stretch its supply lines thin and countering when they're too far interior to get great support.) and Cuba (which the United States basically cut off all ties to and maintains poorer relationships with the countries that did not cut off Cuba ties). Beyond that, the countries physically closest to the United States (by the Crow Flies) are either friendly or neutral (very rarely are they hostile and those that are don't have the capability of supporting that hostility).
These two schools essentially work on some level of another layer of defense. Switzerland, by not taking sides in any international issues means that while they have few strong friends, they have even fewer enemies. The Swiss have made clear that if they are at war, they will not be the aggressor country. They have military strength for sure, they will use it, but their most powerful defense is that anyone who goes to war with them is clearly the bully. It's not so much as spin as it is obvious.
Contrast with the United States. Like Switzerland, their overall goal is to be left alone. Unlike Switzerland, they will have stronger friendships with other countries, but they have to gain something out of it. Most of America's closest allies physically closer to the United States than the threats... consider the cold war... had it gone hot, Russia's avenues of attack are Alaska/Canada or Europe. There are quite a few European countries that would have to fall before they could get enough invasion forces into boats and cross the Atlantic. The United States has always had an underlying desire to keep the problems of the world out of their hemispheres and will be aggressive in doing such. They will be more than willing to help a foreign power, but that help is largely to keep the problem "over there" Solve it, pause it, or redirect it, whatever... just keep it on your side of the ocean. And while the leadership has become more involved, the populous still has a strong opinion of "Not Our Monkeys, Not our Circus" (fun fact, the United States was content to only fight Japan following Pearl Harbor).
In essence, this country of yours would want to hold to the Teddy Roosevelt quote "Speak Softly and Carry a Big Stick." It will have diplomatic power, but not in the sense of an aggressively diplomatic nation. Rather, it will have a booming economy that can allow its citizens to live in comfort, and who it chooses to do business with or not do business with is its lone diplomatic voice. His leader should speak in innuendo that is never threatening. He will always do business in direct line of sight of some cool and flashy piece of military hardware. Should the guy he's dealing with not want to deal, they can at least have a conversation about said hardware piece, which will either prompt the guest to ask where they could get something like that (which should be met with, "I know a guy who can get you one in any color you want... so long as it's black") or make the guy think twice about the benefit of being friendly with someone with that cool toy. And of course the realization that you don't by a thing like that unless you intend to play with it.
There have been examples for a super power been too much internally fragmented to exert its power external. The Holy Roman Empire comes into mind. If the political elites are consumed fighting each other, they will develop hardly ambition to shape the geopolitical landscape. This behaviour will be reinforced, if they perceive the source of wealth and power of their own country to be more valuable than what the world can offer.