I have an 81 that is showing 11.75 volts at the battery and under 11.75 at the choke with the key in the on position.  I did not crank the car yet!  The choke has not been properly operating at this time, see below.  I put a GM crate engine in the vehicle, cut the CCC out but kept the electric choke.

HNY yerself!!
The choke is fed 12v(or batt voltage) key on. The choke coil acts as a heating element. As it heats up, the coil expands, and opens the choke blade. To do this, the coil must provide a ground(resistance), which in turn heats the coil up.
No voltage at the coil would indeed mean a break in the power flow, such as a fuse, or bad connection. This will normally turn on the "Check Engine" light, but if you have eliminated the ECM, your's prolly won't do that.
Now...you have (system)voltage at the coil terminal, so we know there is power. That voltage should be going to ground thru the choke coil, which is what creates the heat that makes it un-coil, and open the choke blade on the car. Whut we've got heah, is, failure to terminate. Apparently, the choke coil is not fully grounding, and that is causing the problems. The coil inside the choke housing can break, or it could have just become loose enough to not fully provide a ground.
You might take the cover off of the coil, and have a peek inside. Sometimes, there is enough corrosion to cause this, too.
hth

Joel:

I've used an Edelbrock 600 CFM w/electric choke on my 327  for a few years and the ground wire went right to a carb stud. That should not be a problem. As long as you've got good ground straps the engine, the carb should be just as good a ground as any other part.

Will do and thanks for the advice.  Not getting back on it till Saturday, but will  let you know!

I had to run a new 12v ignition sourced wire to the choke. The original choke wire on your '81 will not provide enough voltage to operate the aftermarket choke. I believe there is a resistor within the circuit. But whatever the case is, it won't work.

Without looking at the wiring diagram, I believe the choke voltage was provided by the alternator feed, and the choke ground provided by the ECM...I do know a malfunction in the choke circuit, whether by the choke itself, or the radio, will turn on the Choke light.
But I digest...
The choke should have system(12v) voltage to work on pretty much any aftermarket, electrical choke.

What ignition source would you guys recommend and I assume from the beloved hard to get to fuse box?  

If you haven't used them already, there are usually a couple of open ignition ports on the fuse box. With the key in the "Run" position, check with a test light or voltmeter to see if you have power. Then with the key in the "Off" position, if there's no longer any juice, that should be a good 12V ignition source.

The best way to wire an aftermarket choke is with a relay.  An ignition signal turns on the relay which provides direct battery (better yet alternator) power to the choke itself.  And yes, the ground is important.   The common failure is the choke heater in the coil itself.