Dumb question: are you sure the alarm switch is in the off position? For many years I thought vertical was off, but off is actually horizontal. Wasn't a problem when the system didn't work at all but after I started messing with it to try to get it working again, I got battery drain. I have a battery cutoff switch but it's easy to forget and with the drain that the alarm system causes, it would drain in a day or two - not good. Better to fix it right or completely disable the system. I did get it working eventually with a fair amount of tinkering. I now have a functional factory alarm system that I actually use (although it is quite rudimentary compared to modern systems) One of the most problematic parts of the factory system is the switch piggy backed on to the key switch that will trip the alarm system if someone tries to mess with the key switch. Very finicky and if it's not positioned correctly, it will trip the alarm. IIRC, that switch is the same P/N as the headlight warning switch (the one that will make the dash light come on if the headlights don't come up all the way). Also I had trouble with the door switches - be careful with cheapy replacements.
I agree that a battery cutoff switch is a good idea for these cars for long term storage. But to use them to solve a problem that will drain the battery overnight is not a good idea. If there is that much drain, it needs to be fixed properly or at least the offending circuit should be disabled (if feasible). It may seem difficult, but it is possible to fix battery drain on these cars. I can now let my car sit for two months with the battery connected. I can get in, not have to reset the clock, and start it right up. Good luck.
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1976 Silver/Firethorn. L48, 4spd. Original 2 bolt, vortec heads, 9.4:1 CR, Speed Pro Cam: 224/224@0.050, 112 LSA, Eagle Steel Crank.