I'm about to change my monaural AM radio to a retrosound.
The antenna wiring drove me nuts until I realized, that it's not directly compatible with the nowadays usual blue (or blue-white) wire to power the power antenna from the radio.
The antenna control circuit in my 79 LeBaron is just inserted in the IGN-power wire to the radio (see service manual wiring diagram above). The clicking inside the black box (which is connected to the wiring with the black connector) is the relay to power the antenna motor (two wires, yellow and brown) - photo of its inner workings below. Correctly mentioned above, that this is powered by the cigar lighter circuit (20A).
Now, what puzzles me is, how to get a modern radio hooked up to this kind of antenna control setup.
One (relatively easy) solution is, to just connect the (new) radio power to the original red wire, which powers the original radio, keep the original antenna control hookup as is (cut the red wire directly at the old radio and power new one with this) and let the magic of this antenna power control do its work.
But. This would probably just raise the antenna whenever you turn on ignition, no matter if the radio is powered up.
Further, you only have 5 amps for your new stereo (to be correct: and the "lights on" of the electronic clock). That's not much and the wiring (20 AWG!) is only sized for up to 6 amps. So better not just use a bigger fuse, because your wiring will fail over time and trigger much worse problems.
My current plan is, to use the blue wire of my retrosound (motor-6) to power an antenna splitter (for dab+ signal [europe digital radio] / comparable to like sirius digital radio in the US). In this wire I'll integrate the original antenna control box (directly before the splitter). Hoping, that the 40mA the splitter consumes are enough to trigger the control box.
Hopefully, my writing is somehow understandable

I'll try to get some fritzing design for easy reference.
Here's the inside of the antenna control box: