I've never had luck with braid ins. Some how some way they typically get them off within a few days. The longest I have had one stay is a week. These were braided into the under mane closest to the neck and behind where they rub if itching face and ears. I'm on the same page as HLG about halters. Not wearing them without supervision. I personally would leave it with the microchip and not worry about GPS. Being know to and having an active theft ring are two different things. I would think more likely fields where there are not people in and out and houses close would be targeted so they horse isn't swiftly missed. Here many know who belongs where and a wandering horse is returned quickly or penned until owner is notified. It surprises me when I get calls about neighbors not seeing X horse in the pasture and they want to know why. At first an irritation now not so much. We all tend to look out for each other.
Some horse people change their horse, they change their tack and discipline, they change their instructor; they never change themselves.