Like, with the brain we know that the mind is deeply linked to it because it's just very obvious. Brain damage heavily impacts cognition, people lose memories, their personalities change, they lose the capacity to feel certain things or certain concepts - we even have some idea of damaging what area causes what.
Compare this with people losing limbs or sensory organs. Someone who loses their sight, doesn't lose their visual memory, their ability to visualize things, spatial concepts, etc. If these organs were actually part of the mind I would have at least expected some part of it to be lost.
So unless evidence for the contrary comes to light, it only seems reasonable to me to assume that no or at the very least minimal real processing occurs outside of the brain.
If there was some other influence causing changes to the mind, I don't know of it. It doesn't seem like the hormone creating organs are itself is part of the mind, as just taking the hormones seems to cause the same effects. So what else could it be? I guess it's theoretically possible that some systems like the blood stream itself are part of the mind - but there's nothing that indicates this, so I think it's pretty unlikely.
Or, staying closer to measurable things, glands mean that you should expect the personality of a brain being getting a full body transplant can become significantly different, just because of all the new hormone glands they will be exposed to. So in some sense, you are not moving a person to a new body, but creating a new person that will inherit many characteristics from the brain donor (memories, for sure, probably others), and many other characteristics from the body donor (personality traits, such as aggression or how sedentary they may be, very likely some dietary preferences).
Edit: clarified first sentence.
I'm not sure whether the changes would really be large enough to classify them as a new person. Hormone replacement therapy seems like a pretty damn large change, but I don't think I've heard of a case where there's truly radical personality changes. The same goes for other gland issues and their treatment. Though this is just guessing of course.
The same could likely be said for pieces of the brain, if we had a way to synthesize the right substances. What seems much more relevant to me is whether the glands are directly controlled by the brain, in which case they are simply a kind of support organ, just like the heart; or if they have their own signal processing and can "decide" (in the algorithmic sense) to secrete substances based on their own analysis of the internal or external environment, separate from the brain. If so, then I would characterize them as a part of the mind. The fact that their function CAN be replaced by taking hormones doesn't mean that X+testicles would be the same person as X+testosterone-testicles: the part of their mind that decided WHEN to produce testosterone would be gone.
Note that this is all an IF. It's quite likely that the decision to release certain hormones in certain quantities is controlled entirely by the brain, with the glands responding only to nerve signals.
> Hormone replacement therapy seems like a pretty damn large change, but I don't think I've heard of a case where there's truly radical personality changes. The same goes for other gland issues and their treatment.
From what I know, there can be pretty extreme effects from hormone issues, like extreme mood swings and defensiveness related to child birth, for example, or extreme aggression/irascibility related to high testosterone.