I figured it out. I found a thread on the Ford Ranger forum where a guy was putting a Mustang dome lamp into his truck.
The problem is that unlike the GM cars, the Ford lights are switched positive. That is, rather than the door switch completing a ground, there is a module that sends 12V+ to activate the dome lamp when the door opens.
So, like nearly every other project I embark upon, this one wasn't as simple as I had hoped.
I had to make a wiring harness using the stock Ford dome lamp plug and a relay:
Luckily there's plenty of room up in the ceiling to tuck in the relay and wiring.
Here's the old lamp. It wasn't very bright because the lens had yellowed over the years. Plus I didn't like the chrome:
Here's the Mustang dome light installed:
It looks much more modern and is brighter. I plan to put LEDs in it, but this is good for now.