As an Army 42A reservist, how can I attend the RTI at Camp Williams to reclass to the 35 series?

You should definitely be talking to your unit first off. Secondly - do you have a TS clearance with SCI eligibility? If not, you have to have that to be 35 series - especially those two MOSs. If you don't have TS/SCI, you'll have to talk to your S2 as well. You're not going to get to 35F for sure if you don't have an open T5.

First of all, you need to speak to your training NCO. Follow your chain of command as a lower enlisted soldier; I would highly recommend going to your unit and ask them.

There is nothing more frustrating than a soldier going out of their chain of command and asking how to attend a school.

The short answer is your NCO needs to look for an open slot for school in ATTARS and enroll you. It's not possible to do this yourself without the proper access and roles.

PFC Fors did you engage with your schools NCO yet? If you didn’t I highly advise you to do so. In addition make sure you keep your NCOs in the loop.