This is reminding me of the same issues I had with my 89 a few years ago. I was chasing a starting/electrical gremlin and ended up replacing the battery (it was old anyway), installed a new Alternator, then installed a new (non-oem) starter. The truck would start but only after I beat on the starter with a wrench. I figured the new starter didn't "mesh" well with the OEM flywheel. I was still having intermittent starting issues even when I would beat on the starter so I moved to wiring. I bypassed the ignition and used one of those "trigger" starters and it would start every time. To try and isolate the problem further, I re-installed the OE starter with the trigger starter and it started every time. So it seemed I replaced the starter (and possibly the battery and alternator) for nothing.
After doing all that, I came to the conclusion that it had something to do with either wiring or the actual ignition switch. I found a thread on a 240z website where a guy had a similar issue and had trouble finding an ignition switch that fit his car. He did a little write up on how to bypass the switch with a relay and a push button starter. I didn't want to hack up the dash so I found a button that fit in the dash hole that was made for Non-US models that have a handle throttle. I've been driving it like this for almost 3 years.
I have plans to properly fix it at some point. Does anyone know if the ignition switch for 62's works for both automatic and manual vehicles? I have an H55.