It also contains a tracking device to ensure where the citizen is at all times.
GPS uses frequencies around 1.2-1.5 GHz. According to this you lose 4dB/cm in RF power when going through people/meat, thus your antenna must not be buried too deep. In fact, it would be better if it was right under the skin.
Thus the best place for GPS reception would be on top of the cranium. Sorry Will, if you put it down there, you won't get any signal... 1.5 GHz won't go through the body, it will be absorbed.
The obvious counter to this is to wear a tin foil hat, as everyone already knows.
Other places would be on the shoulders, for example.
Now, your tracker has a few issues, because GPS reception is unreliable: it doesn't work well indoors, doesn't work at all in tunnels, and especially not in the rebels' secret underground bunkers that you want to find.
Thus "loss of signal" will occur often, basically every time your faceless minions walk into an underground car park or even indoors.
Thus you can't differentiate between "loss of signal for legal reasons" and "someone put a tinfoil hat, send in the SWAT teams" which makes your tracker less useful.
Also, unless you want to bolt self-aligning satellite dishes on top of everyone's head, the receiving antenna will be tiny, perhaps like the one in a smartphone. Unless you shoot a whole new constellation of satellites into orbit with much higher RF transmit power than what the current GPS ones have, this tiny antenna means the received signal to noise ratio is very poor, and thus the GPS chip will need at least several seconds of averaging to get a proper location fix.
The limits to this are about the amount of power received by an antenna of a certain size versus ambient noise, and this no amount of space magic will give you a better time-to-fix unless the transmitters are made a lot more powerful.
We do it this way for cost: powerful RF transmitters require power thus big solar panels, which are heavy, which require bigger rockets to shoot them into space, which costs money. Maybe no-object once you Take Over The World, but keep this in mind.
So, with current GPS RF power levels you'll need to power up your GPS receiver for quite a while before getting a fix. This means it will use more energy than you think. Having a look here, it will draw 60mW for a few seconds during acquisition.
Also, acquisition requires a much higher signal strength than tracking, it won't work at all indoors while tracking might work if the "user" is close to a window.
The datasheet I linked helpfully describes the modules' logging features, and how to conserve power in a data logging application, but if you want real time logging, less than about 15mW average won't cut it.
And you need real time logging, at least every few seconds, if you want to know where the entrance to the secret rebel hideout is!
This power draw is a problem. Your chances of fixing it with space magic technology are low, because the underlying circuitry will have to include a few RF circuits which are analog and include some hard tradeoffs in the noise versus power draw domain. Even if it's much lower, say 2mW, you still need to transmit often enough, which rules out a thermal generator, as said in the other answers.
However you can always handwave a space battery to power it, or a graphene supercapacitor, whatever.
So, my answer to your question is:
Every one of your minions must recharge their implant every two days. A routine search and interrogation will also be performed on the occasion, of course. Remember to always be nice to your political officer. They're here to help!
Shocking the user when the implant stops working or is removed doesn't seem doable. It would be a lot better to release a chemical if the implant is tampered with, or the user "forgets" to report to the nearest office of the Ministry Of Truth for his recharge. Effects of said chemicals are up to you, from giving the users' skin a fluorescent green glow (which gets them arrested) to making them sick. Lots of plot bunnies here.