Just documenting as I said I would. Settings 1 and 5 don't work. Burris CS recommended the following:
Clean the battery compartment with a Q-Tip and just a little alchohol. Make three or four rotations with the illumination selector. If that doesn’t clear up the problem send it to us and we’ll replace it.
Cleaning as described didn't fix the problem, nor did replacing the battery. Battery compartment showed no obvious problem. Burris was helpful and polite and sent me a repair form, but hoping MidwayUSA would replace it faster, I contacted them but have yet to hear back. If I don't soon I'll send it to Burris.