Is the light on while engine is running or on when off? If on while off, bad voltage regulator, if on while running, use a volt meter check across battery, should read 13.5 to 14 volts if charging, if not, 11.8 to 12.3 should tell you the alt. is probable bad. take it off and have your local parts store check it.
I would suspect the alternator. Inside are 6 diode. The AC current produced by the alternator is run through the diodes and it becomes DC current. If 1 or more of these diodes go out you'll still get some output but not as much current. During episodes of higher electrical demand the current cannpt go up, so the voltage goes down. which is triggering your light.
Have your alternator retested. Hopefully the shop testing it will spin it up and put a load on it. If it still passes take a close look at your battery cables and battery,
<!-- / message -->Can't speak to a 71 for sure, other than that I'd make sure your regulator is OK, then start under the dash to see if you may have another issue, or just remove the bulb if it annoys you
Worth double checking it works before you go chasing your tail.
Also double check that all the connections are properly made, just in case you missed a wire somewhere, or the terminal clamps aren't properly tightened on the battery.
Wouldn't been the first time I forgot to tighten the battery clamps after the job!
double check there are no pinched cables anywhere in case there's a dead short, that would trigger an alt light IIRC
Also, do you have a newer style alternator with an inbuilt voltage regulator ?
If not, the regulator could be the problem