That and coupled with a piss-poor design that overloads the connectors.
IMO, There never should have been the General illumination circuit going through so many connectors. Each connector adds a slight amount of resistance which is dissipated as heat. The connectors are running at the top end of their specs (maxed out).
After you replace the connectors and repair the foil traces & solder joints, you should consider reducing the load on the connectors. You can do this in several ways:
1. Switch out all the #44 bulbs in the G.I. circuit to #47's instead. The 47's draw less current.
2. Remove several bulbs and leave the sockets empty. Good if your machine uses # 555 bulbs.
3. Switch from incandescent bulbs to LED's. You can either go with all LED's in the general Illumination circuit or just some LED's mixed with incandescent bulbs.
Any of the above will greatly reduce the load on the connectors so that they never burn up again and your machine will stay lit.
Oh yes, I almost forgot, anytime you spot burned connectors in the backbox, you should also look at the 4 pin general illumination connector (the one with the yellow and yellow-white wires) down in the cabinet at the power transformer. I've personally seen that one burn to a crisp too.