Here are some early factory wiring diagrams:
http://members.rennlist.org/911pcars/WiringDiag.htm
Mine has two fuse boxes with 8 fuse positions inside. Your electrical system may be different. A yellow wire from the ignition switch (item 2) connects to the starter solenoid (item 1). This is the wire that energizes the solenoid during cranking.
There's another yellow wire at the solenoid terminal that continues into the engine compartment and is the circuit you have an issue with since it either disables the solenoid (harness connected) or allows the starter to crank (harness separated).
According to the wiring diagram, this circuit goes to the following parts:
70 Time limit switch, then parallel circuit to item 66 (starting relay switch)
71 Temperature switch (start)
72 Temperature switch (start assist)
62 is the multi-pin harness connector (your connect/disconnect point)
My carbureted 69T doesn't have this circuit from the solenoid. I'm not an MFI guy, but I suspect the above parts are for cold start MFI enrichment. If yours is MFI, I'd locate and identify each part, then disconnect the yellow wire to each in turn to help isolate the source of the malfunction.
Hope this helps,
Sherwood