After reading some other post on this site about original factory power antenna for the 1981 year I do think the antenna I have is a new or NOS antenna from the description of the after market and the Chevrolet antenna in that post. 

Assuming that the radio signal is getting to the relay and that's causing the relay click thereby signifying  it's being energized.  The next thing you need to do is to determine if the 12 volts is getting to one side of the contacts. You can do that with your test light or you can use a digital voltmeter. You can pick one of those up at a Harbor Freight for less than $10. If you're getting 12 volts to one side of the relay contacts when the relay is energized, you need to check the other contact which would be the one going to the antenna. If you have 12 volts there and that would indicate an open circuit between the relay and the antenna, an antenna connector problem, or something internal to the motor on the antenna.

The service manual should contain a wiring diagram which will be an immense help.

1973 L-82 4 spd

73Shark,  With all the problems the power antenna cause like the one I'm having now and the ones that will arise in the future I've been considering removing the power antenna from the car. I can buy a fixed antenna for a 1980 to 1982 Corvette  from Ecklers for about $74.00 dollars with free shipping. I'm in my mid 60s and I just can't bend and twist around like I used to,  getting to that relay is a problem. I've posted a diagram of all the relays in the storage box behind the passenger side seat and the click I'm getting when I turn the radio on and off is from the metal box on the right in the diagram next to the Blue antenna relay. The Blue antenna plug on the right in the diagram is the power in from the radio and the plug on the Left in the diagram is power to the antenna from the relay. I'm wondering and in your opinion if I leave both the in and out plugs to the antenna relay disconnected will that cause any problems ?  I also want to disconnect my anti theft alarm and at this time have the theft fuse at the fuse box out I'm unsure if that has the alarm inactivated or not,  do you think I would be better off replacing the fuse and unplugging the anti theft module to the Left of the antenna relay ?

Since the antenna power is not working anyway, I don't think you need to disconnect anything. As far as the security alarm, leaving the fuse pulled should effectively eliminate it.

As to what caused the initial power antenna failure, I'm always suspicious when someone works on a vehicle to fix something and when you get it back, something else is wrong. Since the antenna is located directly above the driver side muffler, it would be good idea to check the connection on it.

1973 L-82 4 spd

Thanks,  I just had the muffler taken off and I'm going to look at the wires a little closer on the antenna motor. I also received my shop manual today and did some checking on the wires at the relay per that manual. I can't get the antenna to come up when I do what the manual recommends so maybe the motor on it is already bad. I also ordered the fixed antenna and as soon as it arrives it's going on. To he** with that power antenna. Once again I appreciate your help with this Thanks and take care.

When you get the antenna out, try hooking 12 volts directly to the motor and see if that has any effect. Hope the new antenna has the same coax connection as the power antenna.

1973 L-82 4 spd

I have the power antenna out and yes that's what I'm going to do on Tuesday,  I'll post the findings. No the new antenna has a new cable long enough to reach the radio. I'm going to leave all the old wiring and the power antenna cable in the car, the power antenna cable has a screw together connection just after it gets into the inside of the car. It has a connecting plug for the relay wires  in the same place. I'll just run the new antenna cable in along with the old and up to the radio. 

Well I bench tested the antenna how the service manual recommends. But I used a battery charger instead of a battery. I hooked up the green wire on the antenna plug to the + on the charger, the grey wire on the antenna to the - on the charger, this should raise the antenna. Nothing but a few small crackles as I was touching the connections together. Then I tried the other side of the spectrum, I hooked the white wire on the antenna to the + side of the charger and the green wire on the antenna to the - side on the charger,  this should lower the antenna. Same thing some small crackling at the connections. I unhooked the charger from the antenna and lightly bounced the antenna off the concrete floor a few times and hooked the antenna back up to the charger as if to raise the antenna and guess what,  antenna raised. I then hooked it back up to lower and she went down.  Your guess is as good as mine what the Sam He** that was about or what caused the antenna not to work in the first place but I have a New working antenna. I'm not going to use it simply because of this kind of problems, I'm going with the fixed antenna when it arrives.    

That's what we called a "drop check" in the Navy. . .

I suspect that the coiled wire that drives the antenna up and down was probably stuck and your drop test freed it up. Had it been in an extended or retracted position for a long period of time?

1973 L-82 4 spd

I salute you Mr. Hanna, Thanks for your service to this Great Country. My Father was in the Navy on board the USS Benner World War 2. 

73Shark no the antenna was in the down position and I'm unsure how long,  could have only been at the most 7 days. Like I said after the new mufflers had been put on I don't remember if turned the radio back on. After I had the mufflers put on I had another shop put in new plug wires, plugs and the timing set,  they also adjusted the carburetor. I also don't remember if I turned the radio on then. But I do know that the antenna worked because I had the radio on before all this took place and the antenna went up and down as it should.  It's got me awe, The mystery's of life I guess.  : )