Wushoolay's is a RPPM trinket with an internal CD of 22 seconds in order to prevent the proc chaining/stacking and yielding an absurd amount of intellect.
As for RPPM trinkets in general, they are almost guaranteed to proc in the pull given that you haven't been in combat/they haven't procced for a while before the pull. I noticed this on tortos, where we had some very fast wipes and due to the short corpse run, there was little time between each pull, and I noticed that my trinkets (lei Shen and wush) did not always proc. but whenever we had a longer time between our pulls, say around 5 minutes, they always procced. I do not know how this interacts with unequipping them, but it could be wise to unequip trinkets on trash in order to preserve the proc and guarantee a proc in the pull, should you wish for it.