Actually, you gave me an idea!
There are button-sized Bluetooth GPS loggers. They can record a GPS track, and you can later download the data from them. Since it's freaking GPS, it automatically has timestamps, so it's easy to correlate with other activity.
As a bonus, I think it should be possible to connect them directly with the phone.
BRB, I think I have a ESP-based Tiny Arudino somewhere...
Beware that they take much longer to start since they don't know the GPS coords of the nearest cell tower, nor do they download the GPS almanac over the cell connection. They will however remember the almanac so you can leave it on for 30 minutes and not have to redownload it the next day.
Sad that most of ham radio, which has similar APRS for tracking, doesn't do async or multi-hop.
I have not tested it, but it should be hackable. I have a couple of discrete RAK chips, and I've ordered a PCB with a trace antenna for them.
Or the Mesh Node T114 Development Board V2 (23mm wide).