1997 Blazer won't try to start sometimes

I have a 1997 Blazer 4WD automatic. This past weekend, I started it, drove a short way, then turned it off. When I tried to start it a few minutes later, I had full electrical power, but it wouldn't even try to turn over (I mean nothing. No clicks like when the battery is bad). After several attempts, it started just fine. It did this a couple more times this weekend. I pulled the starter today and had it tested at the auto parts store. It was fine. The gentleman who helped me thought it might be the neutral safety switch. Does this sound right? If so, where do I locate it? Any other ideas?

Thanks.

neutral safety switch is mounted around the shaft on the tranny that has the shifter cable attached. This vehicle also has a starter relay, so that may be going bad. When it doesn't want to crank in Park, try neutral to see if it makes any difference