I was wondering the same question about my regimen; I take testosterone cypiponate and HCG and am currently on day 2 water only. My plan is to continue as usual with my weekly dose; I assume it's best to keep a normal, regulated, hormone level during a fast... I have absolutely nothing to back up that assumption but it just seems like I wouldn't want to put any additional stress on my body during a fast(and depending on how long you've been on hormone therapy that could really cause some problems.
And your question about do people work or just rest during a fast I personally have never been able to rest much during a fast..however, anytime I feel slightly dizzy or tired or anything I'm going to sit/lay down.