360 - Runs perfectly, but dash is dead??

I drove the car to the store (about five miles away), ran perfectly. Spent about 1/2 hour in the store. Came back out, started the car, still ran perfectly, but nothing on the dash worked, except for the headlight icon, which flashed repeatedly (lights weren't on, it was during the day). When I got home, I shut the car off, then got back in after a couple of minutes, hoping the problem would go away. The moment I opened the door, the clicking starts, sounds like a relay clicking at high speed. When I close the door, the clicking stops. When I put the key into the ignition, the clicking started again, and, after starting the car, the dash was still dead (like before).
I wiped down the car, chatted with my neighbor, etc., basically left the car alone for about 10 minutes. I got back into the car, and all of the problems disappeared! No clicking, dash lit up when I put the key in the ignition, and all the gauges worked after starting.
Has anyone seen anything like this?
Thanks in advance.