I debated having the car towed, but I've had what I thought was a similar problem with a bad pressure switch on another 914 and decided to drive it home. The car drove normally and the engine sounded perfect, though the oil light was still dimly staring back at me.
Finally had a chance to swap out the sender tonight and it's acting the same way. Turn ignition switch to "ON" and it's bright. Start the car and it's on, but dim.
It's a very solid dim. No flickering or changes in luminosity depending on engine RPM. There's no engine oil spewing out when the car's on either.

I think there's a problem elsewhere. Obviously I need to make sure I have good oil pressure before driving it, and I'm going to borrow a screw in pressure gauge from my machinist friend before doing so.
With that said, what are the odds that I have low oil pressure? 914s that I've had before with low oil pressure had idiot lights that flickered, usually brightly. If it's an electrical problem, where should I start digging?
Thanks!