If it has been tested as you say, to know that it works on two heads, then I agree, have it looked over.
Even fungus and mold can cause problems with high voltage leakage, and this thing likely put out between 500 and 900V DC. I am mostly a Speedotron guy, but see that Novatron is a made in USA prodcut as well
I suspect the power switch you find on the heads may relate to dropping the light output of the modelling light only so that it's light output can approximate out the way that flash tube power is divided between the channels, and the number of head on the channels. I have not seen a pack and head system ever adjust flash tube outut on the head. It is usualy done by varying the number of capacitors per channel at the pack.
It uses electrolytic capacitors. BIG ones. Read up on 'forming' electrolytics. They need regular TLC from the owner. Yours likely has not been powered up for a long time given the price you paid for it.
Be prepared to plug it in and leave it on untouched for a few hours, then turn it off for a day or so, then repeat.
When these sorts of caps fail, they explode inside and sound like a gun going off. It is not gentle, and the fix is usally not cheap.
Good luck in looking after your new toy.