Green’s Dictionary of Slang

to spend freely and generously.

1899		A.C. Gunter M.S. Bradford Special 53: This Western mine owner has tapped his wallet very freely during the three days of metropolitan life.
1938		D. Runyon ‘Lonely Heart’ Runyon on Broadway (1954) 485: He does not mention his habit of tapping out any time a 4-to-5 shot comes along.