'97 F355 Spider Starting Problem

My F355 was in the shop a month ago for its first 30K with 13K miles on it. It has randomly had a failure to start 3 on three occaisons since the service, while sequencing the key fob so it double beeps. When this first occurred, the dealer suggested I shut the power off and go through the 10 minute warm-up procedure and also to try the red master as well as the black fob I use normally. Yesterday when it failed for the 3rd time, I tried both red and black key fobs - no luck - The car gives a proper "double beep" but then all the dash lights come on including the "slow-down" warning which normally occurs when I have forgotten to push the button for the double beep. I then tried to shutoff the master powerswitch and turned it back on after 15 seconds - with no effect. We checked the battery by turning on the headlights which were bright. I have never had a security system battery failure or loss of power that would degrade that. Finally we turned off the Main power switch and waited 5 minutes to call the dealer again and when we truned the power on, we heard a solinoid click in the right rear of the engine compartment, which we had not heard when we had shut the power off before. Sure-enough it started normally and has started normally three times since.
The dealer says this is typical. *hit happens and some times you just have to re-boot the computer, but they recommend waiting the 5 minutes with the power off for that to work??? suggestions?

 

Which Solinoid is this likely to be and where is it exactly?

 

Does anybody know which solinoid in the engine bay is triggered by the main battery switch when it is turned on? And where is it?