I'm working off my memory of having played a T5 as I'm not an owner, so you know the switch positions far better than I!

But yes, the bridge bucker alone is good because, well, it's alone and it's good. If one of the other pups is at fault, you will not hear the fault because it is not switched in with your bridge pup.
But the other positions sound distorted likely because either the body sensor(s) has failed, or the neck pup has; the former is likely, the latter not so much, but possible, though I don't see how as it really is just a mag pup. And with these pups wired in series with one another (or even in parallel, for that matter), you will have the faulty sound in any of those positions. IS position 2 on a T5 really
only the fingerboard pup? Verify that (what do I know!). If so and you have junk for sound, then that eliminates the body-sensor as faulty.
Likewise, if you have physically unplugged the body sensor harness and you still get the noise, then it surely ain't the sensors! If this is, indeed, the case, then either your neck pup has gone bad, or the preamp has gone wonky. No way to isolate which without replacing with known good components. So yessir, it's time to call the mothership

Edward