Okay, an update. After much, much googling, I've found the following. Apparantly the two wires which go to the Explorer's power antenna come off of some sort of relay, and the antenna is grounded to the chassis. If power is applied to the red wire, the antenna should go up. If power is applied to the other wire, the antenna should come down.
Unfortunately, this isn't happening with mine, so it looks like the motor might be shot (oh, joy).
For those attempting a retrofit, a simple SPDT relay should do the trick. Connect the antenna trigger from your HU to one of the coil inputs (usually 85 and 86), and connect the other to ground (if the relay doesn't contain a diode, it won't matter which one is positive and which is negative). Then connect a +12v source to the "common" terminal of the relay (usually 30), and connect the NC terminal (87a) to the green/yellow wire, and the NO terminal (87) to the red wire. It might be prudent to use a switched +12v source for the power, so there's no chance of a malfunction draining your battery when there's no key in the ignition
When there's no power from your HU's antenna trigger, the green/yellow wire gets connected to +12v, powering down the antenna. When you power on your HU, +12v powers up the relay, connecting +12v to the red wire, powering up your antenna. At least in theory. I believe the motor turns itself off when the antenna is either fully up or fully down.