Pause in startup electric process - auto headlights

[DanSanDiego]

I'm puzzled by this one.
When I start my '03 X5 3.0i, the auto headlights function as expected for exactly 12.33seconds. Then they shut off for exactly 60seconds. Then they function as expected permanently until car is turned off. I have replacesd the RLS sensor (just the sensor and not the prism) but the behavior didn't change.
I am now thinking that something is happening with the startup of the electrical system and it is manifesting a symptom in the auto-headlights.
If I change the headlight setting anytime during the process (the first 1min and 12sec) nothing is different (meaning that if I turn the headlight switch to auto at 10 seconds after starting the car, then the auto-headlights will shut off 2.33 seconds later and turn on again exactly 1 minute after that.
I have measured these times with a stop watch because they are exact and consistent.
I swapped the fuse (#41) and that also didn't change the behavior.
Any ideas on what to troubleshoot??