Your explanations and your pictures and your methods are somewhat confusing. You do have the correct connections on one end of the relay. Also: On the relay itself, the convention from left to right is Load-Battery-Switch, which is what you have. It's obvious that your drain could be horn related. Therefore you need to disconnect the horn and do the drain test. Because the horn seems to be interfering with that test. Then, if you see no drain, you can assume that the horn was the problem. So assuming the relay is good, then something up at the column must is shorting. The horn wire is a ground wire which is shorted intentionally by the button parts. Those parts can touch due to incorrect assembly. I don't know if that is your problem or not. But the horn is your priority after the drain test.
Sounds like you know what you are doing, I guess. I will let others take over. We are getting nowhere.
