Have you checked to see how well the heater core is flowing?  Could be
blocked up.

Get some heater hose at a parts store and then get a female water-hose
connection from Wal-Mart, or any hardware store.  Put the connection on
the heater hose and connect that to the heater core with the other hose
disconnected from the radiator.  Take your "new" heater hose and
connect it to a garden hose, and then hit it with the water on full to
flush the core out.  If you get very little water coming back out the
other heater hose, you may need to have the core properly cleaned or
maybe even replaced.

I wouldn't think the temp gauge would be tied into the heater problem
at all.  The sending unit for the gauge should be in the driver's-side
head, under the exhaust manifold... IIRC, it's right between cylinders
1 and 3, although it could be 3 and 5 (can't remember).  Make sure the
connection is good and that the wire hasn't been burned off by exhaust
heat.  The sending unit is cheap, so you may as well replace it anyway.

Someone will hopefully post a decent method of testing the actual
gauge.  You could just apply voltage to see if it pegs, but I wouldn't
try it until you knew how much it would take without damaging the
gauge.

Not sure on the brake light.  My K5 is an '86, so it doesn't have any
new-fangled computer thingy on there ;-)

~jp