Sleuth does just that. It takes him a little while, considering that this other Inspector doesn’t live where he’s used to going when he wants to visit a space-casing beanpole, but he does eventually get there. Puts his sleuthing skills to use and tracks down the right address, even knocks on the right door.
"Hey, other P. I’m here to make you warm milk and tuck you in so you can get some sleep." He’s talking to the door, of course. He wouldn’t just invite himself in. Maybe if this guy was his Pickle Inspector, but he ain’t, and this one seems to be pretty on edge. Probably from not sleeping and all that. And he might have said he was… hurt? He hadn’t understood half of what had been said one of the last times he’d responded to his message, actually. Something about beat-ups.
"Open the door."