Flashers 67 barracuda
I would certainly check for bad connections in this system, and the switch could very well be the culprit. But you can CHECK the switch.
With the switch on, all 4 terminals should have the same voltage.
This would be a relatively special and expensive switch. You are as likely to find an original replacement as an aftermarket toggle. It would be called a "3 pole, single throw," or 3pst, or maybe, TPST for "triple pole, single throw"
I guess you could also do this with a simple SPST (2 post) switch and 3 diodes