97 4Runner sometimes starts, or one click and no start

I have a 97 4runner 3.4L that recently has been having problems starting. Going back about a week in time to the start of the issues:

This problem first surfaced when I went to turn off the car. After turning the ignition to off, the car stopped but then restarted itself, then off, then restarted itself. So I turned the ignition to on, but the cycle of on/off restart continued. Even in the on position it was running rough. After jiggling the key, all was good again and was able to drive home without issue.

So the next day I replaced the ignition switch and thought I had solved the problem. I didn't have any issues until yesterday. When I went to start my truck, it didn't start, just a loud single click from under the hood.

I cleaned the battery cables/connectors and the terminals, no difference. After playing with the key, specifically pressing the key in hard while turning, it cranked over fast and started. So seems the battery is not the issue.

I thought perhaps the NSS, neutral safety switch, may be a cause of my problem. But after shifting between neutral and park and trying to start at either position, I don't think that is the problem, although that is just my guess. It seems to be all in how hard I press the key while turning.

My question:
So given I've replaced the ignition switch already, what would be my next step in diagnosing this problem? All thoughts appreciated. tia!

Replace the contacts in the starter solenoid. Cheap fix. Check the FAQ thread.

Replace the contacts in the starter solenoid. Cheap fix. Check the FAQ thread.

If the starter is clicking, does that rule out the Neutral Safety Switch as a potential problem?

If the starter is clicking, does that rule out the Neutral Safety Switch as a potential problem?

One more question, should I replace the solenoid plunger as well as the contacts? Or just clean up the old plunger and re-use it. tia.

Just clean the plunger and the area where the contacts sit. Make sure the contacts are perpendicular to the plunger by tightening them with a block of wood in place. Tightening the contacts will tend to rotate them and they need to be held in place, perpendicular to the plunger.

http://www.automotiveforums.com/vbulletin/showpost.php?p=3560360&postcount=2

The solenoid contacts are much more common to go bad than the NSS. I think the NSS will cause no function if it is bad, but I am not sure.

Send me your e-mail address and I can send you a Service Manual. See pages ST11 - ST13