Green’s Dictionary of Slang

(Aus.) a time that will never actually arrive or existed in an uncalculated past.

1895		Crowe Aus. Sl. Dict. 86: Tim’s Eve, a time that will never come.
1914		US Congress Hearings 484: As to trying to make people believe that training of that man [...] is going to make him able to handle a lifeboat , you can do it until Tim's eve — which is neither before nor after Christmas.
1966		T.R. Weiss Qly Rev. Lit. 14 298: ‘I’ve been here since Tim's Eve,’ she would say. Tim's Eve was no time at all , it was the Night Before Never.