I’ve seen a demonstration of this (intelligence community heritage museum, it was public it was part of an RF demonstration which also included remotely capturing screen images by listening to a VGA cable and some other cool stuff), the specific mode of operation wasn’t revealed it wasn’t clear if the RF absorbed by the antenna causes enough current to flow to power something in the cellphone which sends out a chirp or if it’s completely passive and measures the RF attenuation changed from an antenna being present.
It wouldn’t surprise me if older 2G phones could be wirelessly powered to some extent I still remember those inductive LED after market antennas for old Nokia phones. Alternatively even if no logic was powered it might be that there was some sort of a mechanism to deal with unwanted buildup like tying a capacitor that once full discharges back through the antenna which causes it to emit signal, that might be the thing that makes most sense since otherwise you are risking building up enough charge to damage something.
For extra inconspicuousness, make the box look like a flask.
I don’t know if the new phones can still be tracked like this but in the early to mid 2000’s you had airborne pods capable of detecting phones in remote locations even those which were off/without a battery.