Can be a noun or verb.
A fast toilet break which must be squeezed into a very tight time window due to work or personal constraints.
Certain jobs like radio DJ require exemplary timing to be honed.
Judgement is required as to whether the pee time combined with the run each side of it will fit the available window.
Girl: The train is going in less than a minute
Boy: No problem, I'm just gonna run pee.
DJ: (On air) That was The Killers and up next it's Blur with Song 2.
DJ: (Off air, to producer) Damn this song is short, I need a run pee.