If that's an old 500C body, does it have the sync port in the side of the body? If it does, that syncs with the rear baffles instead of the lens and might do the trick. Since it stays closed as long as the baffles are open, it should give the back the sync it needs. It doesn't matter if you are in long B exposures since there's no need to sync to the lens opening - the sensor is just on whilest recording blackness if the lens shutter isn't opened yet.
I never owned any of the chromey C lenses. I've always had at least CF, but mostly CFi, CFe, and F lenses. I've also never owned any 500/501 bodies. I've always had at least 503 bodies and a lot of 20x bodies. The 500c, some 500c/m, and I'm not sure on the 500cm had the body shutters (they were technically used for M sync, not the lenses X sync).
One thing about all of the C lenses (new and old) is that the sync contact are mechanical, and hence prone to oxidation/corrosion. They may close, but can get a high resistance. That is fine to "pulse" a strobe which is only looking for 100ms contact, but extended duration may result in loss of "sync" because the resistance is going up as the spring pressure equals out over a few seconds. The contact can usually be cleaned with something like some 10000-15000 grit material, like what we use to smooth out fountain pen nibs. It's like filing points on old cars to clean up the carbon buildup. I also tend to put a tiny drop of DeOxit red on the contacts to keep them from oxidizing further.
If you can get an ohmmeter and old sync cable, you can put it in resistance mode, cut the old cable and connect the meter across the wires (no polarity, just one lead on the center and the other on the shield), fire the lens and watch to see what it does. It should go down to < 1Ω and stay there. If it goes back open immediately, the contact are opening back up. If the resistance starts to vary, jump, or climb, it's most likely corrosion.