so, I bot a factory tow hitch kit. Installation is pretty straight forward, and the wiring harness design makes it impossible to wire it incorrectly. The kit comes with a relay, but some X3's already have the relay installed in anticipation of adding the hitch later (mine did).
After installation, I am getting voltage to both the running and brake lights as soon as the ignition is turned on. I substituted the relay that came with the kit for the one that was pre-installed in the X3, and I have the same conditions.
BTW - the kit relay and pre-installed relay have the same p/n.
And again, the wiring harness has connectors that let you install it only one way. There's no way to cross-connect or get it wrong.
so. I'm wondering if the service tech has to do something else to the car to have it work correctly, like change a code setting in the car's computer or something similar.
Any suggestions?

Presumably, the trailer has known good wiring?
Could the trailer have been converted to a non-conventional pinout by a previous owner?