I get a new, never before seen (or even noticed on the startup
for that matter) an odd looking warning light under the hot/cool
gauge. Looks like a car diagram with little warning streaks coming
from the rear of the car.

After rifling through the manual, I finally found that it meant rear
tail light malfunction. OK, so I do the test and everything is working
fine. Today it did not come on when I started up this morning but this
afternoon it came back on. Did the check again, and all appears well.
After I get to my destination, I restart and it doesn't come on. My
headlights/tail lights are on at this time, but they were not on the
first time the light came on.

Anyway, before I take this to the dealer, can anybody give me some
clues as to what else may be causing this

 

Determine if the light comes on when the brake is applied.

Typically these cars have a device that monitors bulb current or something like this. If a bulb filament burns out or the bulb socket has a higher electrical resistance due to say corrosion the dash light will trip.

Suggest you check the bulbs, bulb and socket electrical contact area. If a dual filament bulb (brake/tail combo bulb) one filament can break dropping onto the other causing problems.

Some owners just change the suspected bulbs.

On older cars, the monitoring device itself can fail but not sure about newer ones.