I have seen a simple thing like a dirty and clogged Cabin filter that restricts A/C air flow cause the flashing A/C light button. It is designed to do this when there is air flow restriction. My Avalon had this condition and the cabin filter caused it. A simple fix.
After reading your issue... it's a possibililty. Just some ideas ...thinking "out of the box".
Also , the
High pressure switch may be the problem as well. It is often overlooked by many techs. But the Toy Service manual directs one to this switch in the Toy diagnostic flow chart.
Good luck
LT