Frame challenge: Don't make a second brain at all
What is responsible for vision, hearing, taste is in the head, the
second brain is part of the intellect and distributes functions.
Many primitive creatures have more distributed thinking organs than humans, but evolution has decided that this is not actually a good thing for a reason. From a performance standpoint, 2 brains is worse than one. The farther a signal has to travel, the slower you are able to think; so, if you split your brain such that your sensory processing is in one place, and your thinking is in another very separate part of your body, then complex behaviors which require a combination of biofeedback and cognition will take you much longer which will make you in many ways dumber.
This principle is the same reason why Solid State Hard Drives are normally directly integrated with the motherboard instead of wiring them up in drive bays like older style drives. This is because newer hard drives are so fast that the signal delay of separating them was making choke points in how fast a computer could actually interact with its drives.
Make the brain more efficient instead
When it comes to making brains smaller, there are two methods one can use:
- Make the individual neurons smaller.
- Add more dendrite/synapse connections per neuron.
One group of animals that appears to do both of these well beyond the limits of great-ape style brains like humans have are parrots.
Macaws for example have a brain that is about ~21 g with about ~3.1 billion neurons*. But, their level of intelligence is almost identical to Chimpanzees who have brains that are ~384g with ~28 billion neurons. This means that an individual neuron in a parrot brain is about 1/2 the mass of a chimpanzee neuron, but packs about 9 times as much processing power.
Not very much is understood for sure about how a macaw brain is so much more efficient than a chimp brain, but one key factor seems to be that their brains have more dendrite/synapse connections per neuron than ape brains do. Since the vast majority of a neuron's mass comes from the cell body and axon, it is pretty easy to add a lot of processing power per mass by just adding more connections per cell.
Now let's look at how the human brain fits into all of this: The Human brain contains ~86 billion neurons at a mass of ~1232g. This means that human brain cells and chimpanzee brain cells are roughly the same mass. Being so evolutionarily similar to chimps, we presumably also have similar numbers of synapses per cell . So if all assumptions hold, it seems very likely that the human brain could be optimized to have cells as small and synapse rich as a macaw yielding the equivalent processing power of another 23.5 kilograms of brain mass. But more importantly than just having more connections to work with, this bird brain could remain small and entirely inside a human size cranium which would keep your neural paths short enough to not inhibit your thinking speed.
When you consider the actual shape of the brain itself though, it will all be determined by what aspects of the superhuman mind you are trying to enhance. For example, if you just want them to be great problem solvers you could make the frontal lobe proportionally larger. If you want them to have good situational awareness and memory, then emphasize the temporal lobes, so on and so forth. Below is a very basic diagram of where certain things happen in the brain which you can use as a reference point to change proportions in comparison to how your superhuman mind has been enhanced.
*All neuron counts in this answer are based on total brain neuron counts SEE TABLE 1; so, these numbers may seem much larger than some sources you will find online that only cite the number of certain kinds of neurons without making their distinctions very clear.