In Home Tracking Device Suggestions?

I was pestered by my local elderly services regarding a misunderstanding that my mother, living with me in a private home, had been 'wandering' (medical term - eloping)
Luckily the person that had the most authority in regards to pestering me was also very intelligent and objective. He did however start to suggest a GPS device, before i explained the misunderstanding.
(My mother was moreso bored/covid-lonely, and would go outside with the explicit intention of finding some nice people to bring her home)
But yes this shouldn't be super hard to google.

As a techy I can offer this:
There are many technologies for tracking, and many contexts for it, some surprisingly mundane.
For example the auditing of 'logistics' organizations, aka UPS/FedEx - and their industrial equivalents. i know for that RFID technology is used, which is much much simpler, and smaller, than GPS technology. RFID is what they put in those tags that you can't remove from clothing in a store to prevent theft. But there's a type of RFID that has up to a 100 mile radius, and still, something barely the size of a little sticker is all that's needed. And unlike GPS, it wouldn't matter if the sky was obstructed.

You can get a family plan via cell phone provider that have specific products that would allow the manager of the account to track elderly parents. Or dogs/cats, and even children!

I don't think a metal detector would work well; depending on its strength, it might locate everything with metal, and cause confusion unless you had a specific tracking device, the kind seen in spy movies.  

A compass can provide you with locations, but I'm also not sure it's really appropriate unless you can find something your GF could wear that could be tracked with a compass, as you'll probably need some kind of signal for the device to lock onto.

Have you contacted any companies that provide life-alert pendants, and specifically ones with tracking ability?    That's where I would start, but be aware that some years ago some switched to tracking devices linked through the Internet, so the facility would (or probably has) Internet linkage for the residents.

Another issue is whether or not your GF would remove the device.

Hikers use various devices and can locate specific areas more accurately than life-alerts, but these devices are also fairly expensive, and need some acquaintance with their capabilities in order to be used successfully.

Look over some of these hits and see if anything could fit your needs:

https://duckduckgo.com/?q=tracking+devices+for+interior+buildings&t=h_&ia=web

I think that the interior building tracking devices are going to be sophisticated beyond what you need, and also that they might be a challenge for anyone, let alone an elderly person, to use.  

There's a woman here who's very tech knowledgeable; I'm P'Ming her to see if she has any suggestions.

Oh...just thought of something...in our first experience in a rehab facility, the staff used some type of tracking device for the wanderers.   This was back in 1999, so the technology probably would have been much simpler than the array of devices today.

Memory care units might have some method of tracking.   You might research local facilities with memory care, and contact them to see if they have any suggestions.

This is rather simple, but is it possible or appropriate for them to "wander" around the facility together, just to spend more time with each other and as a side benefit, for your GM to keep track of your GF?

My 3 yo grandson "the Raccoon" wears a JIOBIT, his mama sewed hooks into all his pants and he goes nowhere without his jiobit snapped into the clasp.

She has a tracking device on her phone and I know the tracker works for about 1/4 mile or more. It's set to go off if he wanders too far (actually, if he leaves by the front door--it's pretty techie).

When I babysit she just adds to app to my phone so I can traack him if he goes outside. I imagine your dad does not move as fast as the Raccoon, and this has saved us a LOT of worry, as he doesn't care where he goes.

I imagine it's relatively pricey, but he's precious to us and doesn't come when called. He may be wearing this in Kindergarten :)