Looks like I may have to try and glue mine back together.

http://corvetteparts.com/item/switch-heater-air-conditioning-ambient-temperature-sensor-1968-1973/?d=43801&itm=Switch

Just found the part number in my 72 assembly manual.  3917359.

I noticed in the link you posted, that that part is for '68-'73....interesting. Don't think I've ever even noticed one. Gotta look at my '73 AIM and see if it shows it, and if it's the same part #. I've seen them on other cars, but never noticed one on a Corvette...but then again..I've never looked for one, either!

http://corvetteparts.com/item/switch-heater-air-conditioning-ambient-temperature-sensor-1968-1973/?d=43801&itm=Switch

OK, glued the silver button part back on to the black mounting plate with epoxy.  Put her all back together and it still pegs the ammeter right.  So I started feeling wires.  Followed the orange wire all the way back to the inline fuse to the horn relay.  The orange wire does not get hot.  The red wire from the horn relay to the inline fuse is pretty warm, and the inline fuse holder is hot to the touch.  Does this tell you electricians anything?  There is a 30 amp fuse in the holder. 

Yes...it tells us there is too much resistance in that circuit. So, we're back to the blower motor drawing too many amps...
If you can dis-connect the blower motor, turn the blower switch to "High", and the gauge responds correctly/normally, the blower motor is the problem. IF, however, you disconnect the blower motor, and the gauge STILL pegs, there is a short int he blower motor/blower relay wiring.
My bet is on the blower motor....

Pulled the power wire off the blower motor and the gauge needle never moves in any switch position (no deflection either way).  I guess that's means it's the blower motor.  Is their any way to fix this short of buying a new motor, or are they a throw away item?

'Nuther electrical question.  The Transmission Controlled Spark system is not on my car anymore but the wires are still there.  Should I jump these two wires together?  Or make sure that they don't touch each other.  Or does it even matter.  They look like they burned from heat or a short a long time ago (before I owned the car) and the exposed wires may be touching each other.

Blower motor is a "replace" only item. Nothing you can do to repair one, that I know of. 
 One last-ditch effort check, before totally condemning it...make SURE the blower motor housing has a good ground. Run a separate ground wire to it from the frame, or engine..anywhere that you know will give it a good ground, and see if that makes any difference.
 The blower motor wiring on one of my Cads was melting, and was keeping the blower from working right all the time. I bought a new($$$$) motor for it, but never installed it. I found the ground circuit for the motor was just barely making any ground at the connector, and the wiring was getting extremely hot. I ran a new, separate ground wire to the connector directly from the engine block, and that solved that problem. I now have a brand new blower motor in stock, if I ever do need it....

As far as the TCS, if the timer is gone, jumping the wires at the connector will prolly give you full-time vacuum...all the time. You may not want that. The system was designed to only give full vacuum with the trans in 3rd/4th gears only on the 4 speed. The timer was used to "delay" the vacuum coming on for about 20-30 seconds after shifting into 3rd, or 4th. Some years, it only worked in 4th. With the system working, if you let the engine idle, you can put the shifter in 4th gear, and in a few seconds, the engine will idle up as the vacuum kicks in. It's a neat way to test to see if it actually works.

I'll try the better ground thing.  As far as the TCS is concerned, it's all gone except for the wires.  No vacuum switch.  My distributor advance comes right off the carb.  I just don't know if it is OK if he wires are touching each other.

I would assume none of the wires has voltage on them. If so, then it would be fine to leave them as they are. If you do see voltage, then just tape them up, and hide them somewhere. 

Oh tay, ran a ground from the frame to the  F&#$(^%$ blower motor and it still pegs the ammeter on high.  So....where is the best place to buy a blower motor.  I know all the Corvette catalogs have them, but since it's a generic GM blower, can I get one at a generic price somewhere?