I wish you the best of luck on this headache...
It is stories, and previous experiences like this that make me do what I do when I tackle a project. People end up tearing their hair out over something that was supposed to be as simple as hooking up an adapter to a factory harness...
I guess I am more interested in what things can do, more than what they are designed to do... For me, it is just easier to start from scratch and design it all, modifying the system design as needed once I am in the thick of it... That way there is no confusion of what wire is what, and "where does that one go?"...
Plus, this way I can make improvements along the way, and if I find some system like the OEM power antenna that I want to use, I can science it out enough to get it to work with what I have in my design...
All this is no consolation, or help, for your current predicament...sorry...
On a more specific note... That power antenna relay has several more "control" and "sense" wires running in and out of it... Again, having never seen any OEM schematic, or pin out diagram for the module, it is hard to say for sure if there is anything else that is preventing your antenna from working the way it should...
This is why I put it on the test bench. I knew that if I found out what pins required constant power/ground, and what pins were the outputs to the antenna itself, all I needed was to find the other pin that required voltage to trigger the module to do what I wanted it to...
I knew (if I had to) I could cut all the rest and know that the antenna would go up (or down) when my new stereo told it to... I did not care about any other OEM control sensor or timing circuit having a say in my antenna usage...in fact, I wired the entire A/V system to direct voltage (with circuit breakers that could be manually tripped and reset) so I did not even have to leave the key in the ignition to jam tunes anywhere...
If I had the time, and a spare module, I would create a tech bench write-up worthy of a sticky... Alas, I do not...
Good luck young grasshopper...