Eating before blood tests are mostly for cholesterol tests. I don’t think that eating prior to your blood test for HIV and syphilis, is going to make a difference in the outcome.
I went to The China University Hospital in Taichung. They are very friendly and efficient. The whole thing took like 15 minutes. X-ray for TB. Blood for HIV and syphilis. Pooh Pooh for e coli and other bacteria. I couldn’t perform so they gave me some liquid (possibly water) to squirt up my bum. Needless to say it worked. They also checked for Hanson disease (whatever that is). They just give you a look and say, ok no problem. This exercise was 2200nt and you have to take 3 pics with and wait a week for your results.