I fixed it!
@Robin Guymer I know you were having the same issue with one of your bodies so maybe this will be of assistance to you. It took a little bit of poking around to figure out the mechanism that causes the T setting to lock into place, and while I don't completely understand it, I figured it out well enough to fix it.
Luckily I had one body in which the T setting worked fine to use as a reference. So first, take the top plate off of the film advance side. Then, look at the small opening on the poserior side of the shutter release button.
There are two small bars that you should be able to see. There is a small hook shaped one on top (the shinier one) and a flat bar (the darker one). This shows what they should look like when the shutter release is set to the middle or L (not T).
This next photo shows what the two bars should look like when set to T. The small hook like bar moves slightly (slightly!) and makes contact with the darker bar.
Then, when the shutter release is pressed, the hook grabs the bar and holds it closer to the shutter release, and should look like this:
The hook is released when the selector is changed from T.
So, again, this is what it SHOULD look like in my body that was working. My body in which the T setting did NOT work looked like this:
Pretty obvious that the hook and bar are not where they are supposed to be. In fact, the bar was pretty loose. (side note, this is the same bar as the one that locks the camera, it is just wrapped around a small post under this middle plate. Part #266 if you're following along at home).
So, figuring I had nothing to lose, I bent the bottom bar back close to the shutter release to see if I could get it in a position where it could be caught by the hook. Now, I really mean bend it. It doesn't bend easy. I really don't know what caused it to get out of whack in the first place. But, once I bent it back into place, the hook was able to catch it and the T setting started working again. I tested it a bunch of times before putting it back together and so far so good. It even works when using the self timer for the exposure. So, Robin, hopefully this works for you too! It should be pretty easy to see if those two components are not where they are supposed to be.