If I have my child carry a GPS, how do I balance it with their independence?

It's easier to reconcile if you think of a GPS or tracker not as a tool that takes away freedom but as a tool that safely widens the range they can manage on their own. First, explain to your child too that it's "so we can help when you're in trouble," and use it with their consent where possible. Narrowing its purpose to locating in emergencies—rather than closely monitoring behavior—preserves trust. As they grow, gradually loosen the range of supervision and, alongside, build the skills to contact and cope on their own (a phone, an SOS card), so it doesn't tip into dependence on the device.