Counting Multiple Occurrences of Text in a Cell

Looking for the most efficient way to determine the position of the LAST occurrence of specific text in a cell. So, if A1 contained AbcdefgAhijklmAnopqrstAuvwxyAz, and my criterion was "A", then I would like the formula in B1 to return 29.

It's annoying that neither FIND nor SEARCH has an "occurrence" option. I can build a compund formula using multiple uses of FIND, but it's hugely inefficient since I don't know what the maximum number of occurrences will be.

Thanks in advance.