When it does it again, Use a test light (with the wire clipped to the +side of the battery) and probe the neutral start wire on the starter relay (not the yellow wire)
The light should light if grounded at the NSS switch.
If it doesn't, pull off the plug on the tranny, then probe the center pin.
If it lights up, the plug or wire is bad. If it doesn't, your NSS switch isn't being grounded by your shift lever inside the tranny. The center pin goes all the way through to touch metal on the shift arm.
Pushing it in only closes the circuit between the 2 outside pins to turn on your reverse lights.