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Bob -
I think more likely, that the straws that stick up from the petcock inside the tank have fallen off. So, when you're on the "main" tank, in fact you're drawing from the bottom of the tank. On this page:
http://w6rec.com/duane/bmw/petcock/
you'll examples of these tubes. I think you're going to need to pull the petcocks and confirm.
When you've run out of gas, how many gallons did it take to fill the tank? If it took around 6 gallons, then the above is the problem. If it took say 4.5-5 gallons, then you still have something going on. Could be that the straw for the "reserve" is plugged.