Hi, Viv, and welcome to TP. I hope you find some helpful advice and information here.
You may want to have a search on here for GPS trackers as I'm sure there have been past threads about this.
I can't give any specific recommendations for brand names or devices, but have seen the following strategies mentioned:
-using the GPS in a person's mobile to track them (must have phone, phone must be on and charged)
-putting GPS tracking devices in a person's purse, if they always carry one particular purse, or the pocket of a coat or jacket, ditto. However, people have reported that their family members have found these devices and discarded them.
-sewing the GPS tracking device into the lining of a purse or jacket; I think eventually the batteries or power source would wear down and you'd need to replace it, plus of course, if they don't take the item with them and/or lose it, you can only track the item, and not the person
-putting a GPS tracking device into a shoe, although I don't know how that works
I have also seen comments from those who have somehow registered their family member (officially or otherwise) with the local police.
I hate to be the voice of doom, but wandering is not an uncommon symptom with dementia. Have you thought about what will happen when she does not, or is not able to return home? Or if she were to suffer an accident or medical emergency while on walkabout? Might there be repercussions if your mum has been gone for hours, in terms of not taking medications, not eating/drinking, or being inadequately dressed for the weather?
Please understand I am not attacking you or criticizing you in any way. My mother was diagnosed with dementia after a hospital stay prompted by being found wandering in January, very early in the morning, disoriented, with no coat in very cold weather. She'd fallen and had a black eye and bruises all over. If she'd wandered to the main road/highway she could easily have been hit by a car; if she hadn't been found by a Good Samaritan she likely would have died of exposure. I would not want that to happen to anyone.