All of this was made clear, with lyrics and quotes, in thread 4070 (post by Dicho): Help Hoolihan Old Paint

Non-westerners confuse the two terms, "Hooleyann," a roping term as described above, and "Houlihan," which usually means to throw a whing-ding or celebration, or paint the town red.

"Houlihan" in rodeo also meant a now barred bull-dogging practice where the performer leaped forward and alighted on the horns of the steer to knock the steer down without having to twist him with a wrestling hold. See "Western Words" by Ramon F. Adams, 1944, p. 79.