This question arose at my husband's office, and I said I would consult all you experts:
"If you or Betty have/has any questions, please call me."
My instinctive answer to this was "have," but I couldn't really explain why I think the "you" form of the verb (have) should take precedence over the "Betty" form of the verb (has), unless it's because you could think of it as having parentheses around "or Betty." However, the more variations I consider, the less sure I am of how to explain the guiding principles.
If either you or Betty have/has any questions . . .
If you and/or Betty have/has any qeustions . . .
If Bob or Betty have/has any questions . . .
If either Bob or Betty have/has any questions . . .
If Bob and/or Betty have/has any questions . . .
If anyone has any questions (obviously not have, because anyone)
If any of you have/has any questions (have inplies only one questioner; has implies several)
Opinions, anyone? Thanks.
(edited to correct a typo)