Timpani : noun A timpani is a cup shaped metal cylindrical, without foot.
Win the timpani: win the jackpot, the bingo, the jackpot; to succeed: to arrive at the top (see below the origin of this expression).
Blow up the timpani: win the jackpot.
Head: having a glitch in the cup: being a little crazy.
Get into trouble by dint of clumsiness.
The expression "Get the cup / the egg cup / the coconut palm": to obtain a disputed thing, an important result - Getting into trouble by dint of clumsiness.
The greasy pole is this post, coated with grease or soap, from the top of which various objects and food were suspended. The game was then to climb the mast and whoever managed to get part of the strut could congratulate himself on the thing: he had obtained a sacred result.
Hence the primary meaning of this expression.
Among the suspended objects, one could find a timpani or an egg cup, hence the use of these words in the first two variants of the phrase, the third (the coconut tree), being only an amusing deformation of the second.
By antiphrase, the expression has also taken on the second meaning proposed, the person concerned having succeeded in “winning” trouble thanks to his constancy in clumsiness.