It seems like you've pretty well isolated it to the ignition switch. If the ignition switch is in the dash this should be quite easy to troubleshoot and fix.
I did some searching and didn't find a switch that was clearly from a '67 Camaro, so what follows is somewhat generic. Many of the switches I found had more than one terminal for the same circuit (for example there might be two terminals for the ignition or the +12 V circuit from the battery).
There are probably four circuits on the back of the switch:
- Circuit 1 will be +12 V and hot all the time. This terminal may be marked BAT. This should be a fairly large wire.
- Circuit 2 will be hot in the Acc position. This terminal may be marked ACC.
- Circuit 3 will be hot (possibly along with 2) in the Run/On position. This terminal may be marked IGN. On some of the switches I found there were two ignition terminals that were not common, it looks like one, labeled IGN1 was used to feed power out to an external resistor which came back on IGN2 to feed the coil.
- Circuit 4 will be hot in the start position (along with 3 and probably 2 as well). This terminal may be marked SOL or ST.
There are also switches that use a ground position (GND or GD) to test the "idiot lights."
If you put key in the Run position and jump from wire 1 to wire 4 the starter should run. Try that when the problem next happens, if it works reliably that pretty much rules out anything but the switch. (In case it is not obvious my numbers are made up, the actual markings on the switch will be different).