Ah, I see now!
When I heard Severed Head's Dead Eyes Opened on the radio last year (and later bought a copy), I was surprised - it didn't match what I remembered.
Now, after sorting through things in the garage, I've found my original tape... only to find that it's not really an original. The cassette single is for a Dead Eyes Opened Remix and doesn't contain the original song at all.
Mystery solved. Memories returned.