Does 35P go to NTC or JRTC? If so, what do they do and for how long?

If you unit goes, then your fanny goes to, don't worry the MOS it is what the UNIT does.

If you are in a tactical unit, you will go during 4 week rotations. You could even be stationed there for 3 year tours.

Are you asking as a rotation or as cadre being assigned there? Because the answer is yes to both. PCS is 3 years, and you could do anything, from developing scripts, to providing injects, or training. As a leader you could be an observer controller. Going on a rotation, well, you'll be doing your Critical tasks. Honestly it depends on your language and what your unit is gearing up for.