1. Cruise control won't turn on or engage.
2. Glove compartment flashlight accessory plug has no power.
3. The navigation display and radio power flicker on and off on their own.
All of these issues appeared to be somewhat sensitive to vibrations at highway speeds. Things would randomly work then cease to work without warning.
The culprit turned out to be the electrical part of the ignition switch. This article shows the steps involved in removing and replacing the component. Total time involved was approximately two hours. Now that I've done one, I think it could be done in 30-45 minutes. Hopefully, the photos below will prove valuable if you ever have to do this.
The only tools you'll need are a 10mm socket, a philips screwdriver, a small flat-blade screwdriver and a T-25 torx ratchet.
The electrical part of the ignition switch. This is the part that we're going to replace. It's located under the left side of the steering column. You don't need to remove the the steering wheel to replace it, though.
The new part (BMW part # 61 32 6 901 962), $39 at The BMW Store.
Lower the steering wheel to about the halfway point and move the seat all the way back.
Disconnect the negative terminal of the battery (located behind the carpet in the right side of the trunk) using a 10mm socket.
Remove the philips screw holding the lower half of the clamshell around the steering column. Don't lose the plastic expansion rivet.
Now do the same for the philips screw holding the upper half of the clamshell.
Press in the sides of the lower half of the clamshell to release it from the upper half.
Pull the lower half out slightly to reveal the leather skirt, which is attached by simple pop rivets.
The lower half of the clamshell, fully removed.
Lift the upper half of the clamshell up and out.
Pull the latch to release the electrical connector.
You'll notice that there's a black plastic housing around the rear portion of the ignition switch. It needs to be separated in order to remove the ignition switch. To do that, two T-25 torx bolts must be removed, one on top and one below.
Once the black plastic housing is out of the way, you'll be able to see two red dots underneath. Scrape away the red paint to reveal the retension screws. Loosen them approximately 1/4" with a flat-blade screwdriver, but don't remove them. This will free the plastic ignition switch so that it can be removed.
With the black plastic housing out of the way and the two retension screws loose, pull the switch away from the steering column.
The old part (above) with the new one (below). The new part is black instead of white, but otherwise looks identical.
The old part on the left, with the new part on the right. Use a small, flat-blade screwdriver to twist the center shaft of the new part to match the old part so that it will align properly when installed.
Install the new switch and reverse the steps to reassemble everything. I'm happy to report that the new part has fixed all of the intermittent electrical problems that we were having.