1999 Other Saturn Models Intermittent no-start

Engine Performance problem
1999 Other Saturn Models 4 cyl Front Wheel Drive Automatic

1999 sc-1 100k miles. My son's first car. Didn't start one day. Would not crank. Not the battery. I jacked car up, got under the car and whacked the starter several times. The car started. Figured bad starter. Replaced it. Couple of weeks later, same problem. After a ten minute drive, every once in a while, it would not start. All the bells and lights and whistles would come on, but when the key is turned all the way to start, engine would not crank. Nothing at all. Then, miraculously after 15-20 minutes, the car would start and run perfectly.(Could have saved starter $) This has happened several times during the past 2 months. My mechanic says it has to happen for him, for a diagnosis. Unfortunately, it never does. My son is usually at school or at the store when it happens. He waits the 15 minutes and it starts. I did notice one thing. After it does not start, if you turn the key to off and remove the key, a clicking sound, not unlike a turn signal, can be heard coming from the passenger side of the trunk, rear seat area. Stuck relay? It "clicks about 10 times then stops. Have yet to locate exactly where sound is coming from. Don't know if one thing has to do with the other but I'm dumbfounded. Any suggestions?