played at the Post Office when Jay opens up the machine and there's an alien inside sorting mail (or whatever)? It's sorta punk-metal and the chorus seems to be saying "Deceiver," but I'm not sure.

Yeah, that's the one; I just listened to it on youtube. Thanks! When the singer screams "Speeeeeeed demon!" I thought he was saying, "Deeeeeceiver!"
Anyway, it definitely changed my mind about Keel, as I thought they were some wimpy 80's hair metal act. Hair metal, yes, but obviously not wimpy, lol! Nice gritty vocals with a primal flair; and definitely nothing like, say, Dokken (who I like).
By the way, a friend let me borrow the cassette back in the mid-80s (THE RIGHT TO ROCK) but I obviously didn't give it the chance it deserves as I was into the heavier side of metal at the time (Death, Bathory, Slayer, Metallica, Death Angel, Sanctuary and so on).
"I don't see any method at all sir."

It's "Speed Demon" by the band Keel. A "blink and you missed them" metal band.
If I agreed with you, we would both be wrong!