Can a person fix a "throw-away" (non-ballast/dual transformer) fluorescent light fixture?

My 48" garage fixture doesn't work on side. It does not have a ballast/silver little canisters. It is run off of 2 small transformers with a little breadboard containing a ceramic capacitor and some resistors. When I took the thing apart, I wasn't sure if the transformer on one side ran bulb 1 or bulb 2. Or if one transformer was in charge of both bulb sockets on either end. To me the wiring looks as if I would not be able to take 2 "one-bulb working" fixtures and make a "2 bulber" without having to throw both the onesies away and spending $ for a new one.