I put it into gear and it dies.

no, not the bulkhead connector, I disconnected the pin connector the ignition switch wires go into.
I just touched the bulkhead connectors with the probe and it lit up the test light.
I would like to take out the bulkhead connector and clean them all, but when I tried to do that before, it would not come out and in the interest of not breaking it, (since it is 50 year old plastic) I stopped.
Gotchya. You could have very well wiggled the back side of the ignition switch enough to restore the connection. In any event, it won't hurt a thing to take some time cleaning all those connections, I don't believe.