Some of this depends on how you want to study.
Although not wholly the case, neuroscience tends to use methods at the micro level (eg., electrophysiology methods, micropipette or whatever that’s called, etc). I don’t know if a single neuroscientist that studies anything as broad as mental illness. Most study very small areas like purkinji cells in the X layer of Y. The smaller areas of study are usually used to infer applications to mental illness. Famously, this is basically the career of Eric kandel (who is a physician). That being said, there are neuroscientists who do bigger anatomical or gross physiological studies such as the danish neuroscientist who famously discoversed the glymmphatic system like 5 years ago.
Neuropsych studies tend to focus on cognition at the level of the person. Most studies have small areas of focus, similar to pretty much ever science. So you see tons of articles about a specific area of cognition in X illness process. Imaging is used, but tends to stay in medical schools due to cost. There are absolutely neuropsychs that do not do clinical work. Stephen Rao, a neuropsych who does see patients, did a series of studies using fMRI about the disease process of some neurological illnesses. Bigler does similar imaging stuff, as does Kiehl. Because you’re dealing with people, you need clinical experience in training at a minimum.
Epidemiologist have other methods at the more macro level. To my knowledge, there is not a huge neuro emphasis.
I hesitate to say this, but there is always Division 6 of the APA, which is termed Behavioral Neuroscience. Purely academic. Combination of behavioral experiments and neuro experiments. Highly reliant on animal models. I trained under one of the leadership guys in undergrad. Fascinating stuff, but it pays poorly and the lifestyle wasn’t what I wanted. Does not lead to ever being licensed. Might be what you’re looking for.
You would be well served to look into the lifestyle of a research scientist. You usually do not get to pick where you live for a long time.
Finally: medical school. Even a research physician makes more, and has better options.
Other things to check out: the society for neuroscience.