During the days after Here There Be Gerblins, Lup absolutely refuses to be let go of by her brother under any circumstances. However, due to her limited power in this situation, this manifests as the Umbrastaff falling over and rolling in Taako’s direction whenever he tries to set it down. Taako, presently in his Simple Idiot Wizard phase, fails to recognize that this is Not Typical Spellcasting Focus Behavior.
During the boys first night at the Bureau, the Umbrastaff won’t stop falling against the ladder to his bunk no matter how he sets it back up again and eventually, when he reaches down to fix it yet again, it turns and hooks around his wrist not letting him go. His reaction is simply, “Oh hey little buddy, wanna sleep with ol’ Taako do you? Hey I can’t blame you, who wouldn’t!” and pulls it up into bed with him and sleeps with the Umbrastaff like it’s a teddy bear.
It takes days before Lup lets Taako put her down and several weeks before she lets him out of sight when he’s not holding her. She almost panics when they ask for the boys weapons upon boarding the Rockport Limited and was never happier that she made her magic-absorbing superwand an inconspicuous umbrella than she was at that moment.
Everyone else just sort of accepts that Taako now has a magic umbrella that he has to hang on the towel rack when he takes a shower so it doesn’t constantly knock against the door of the bathroom for the entire time he’s in there. The best guess anyone has is there’s some charm on it that tied the Umbrastaff to it’s owner and a bit of that charm transferred over to Taako. (Lucretia secretly wonders if Lup had it charmed to find Taako if she perished, or if she charmed it to return to her and with Lup not present, the Umbrastaff thought Taako was close enough. Either way Lucretia is glad some part of Lup found Taako again after all these years, even if it’s not under the most desireable circumstances, unaware of the true extent to which she is correct.)