What is the Army regulation regarding off-duty employment?

Sometimes, your unit should have a policy about employment. If they dont, it would default to the battalion or brigade level and on up. I was a paralegal for the army and often we were task to review unit policies about employment do and donts and whatnots. ask your S1 for a copy or if they know who's policy they follow. On top of that, you will need to get permission from your CO to obtain off duty employment. Check the Joint Ethics Regulation and search for "employment" and also FM 27-14 might have some info for you.

I found an old AR 600-50 from 1988 that covers this (paragraph 2-6). However that AR I'd not on the public version of APD, so I do not know if it still is applicable or if has been superceded by something else (maybe 600-20?).