Update (solved, well 'solution' anyway).
In researching the Pass Key Fault, I found several instructionals on how to perform a proper (resistor) bypass. I figured for the cost of a resistor, it was worth a shot. Well, with the VATS column connector disconnected, and the correct resistor (680Ω in my case) in place, the car starts right up and the warning light is gone.
While it's now working, and I'm content with the 'fix', I didn't actually diagnose what went wrong... I tried my spare key (to see if the VATS resistor on the key was the problem), and the spare key yielded the same results as the primary key...
Anyway, thank you all for your help! For anyone following along, don't be like me. Always disconnect your battery!
1996 Impala SS
1996 Caprice sold