Discussion Forum—A Way with Words, a fun radio show and podcast about language

The phrase is Tossing one's cap through the door and if it's not thrown back it's safe to enter. This has variants of course, but I can only trace it back to Irish derivation. But where in Ireland? It sure doesn't seem gaelic to me. I can find recent or popular use from Michigan-Wisconsin in comedic routines but it seems to have a richer history.