Green’s Dictionary of Slang

(US tramp) to make a false show of religious belief or action to gain handouts from a religious mission.

1936		K. Mackenzie Living Rough 206: To get anything from them, they want you to nose-dive. I wasn’t going to get on my knees and nose-dive with a bunch of mission stiffs.
1961		E. Bendiner Bowery Man 39: Some claim that they were raised on prayer, but they resent being required to ‘nose-dive’ at this late stage [HDAS].