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If you do, don't every let her know it is there, and don't use any evidence from it in court. If you find something out, go to wherever and initiate some other type of surveillance or find some other proof to back up what you find.
It might be that she just likes going to the mall. Or maybe she's a reader and spends a lot of time in the library. Maybe she has some girl friends and the play cards. Don't assume too much without any facts.
Some people are just very private with their personal time and don't see why other's need to know every single detail. This can place a huge burden on a marriage, even one that might otherwise be able to be saved or reconciled.
Legally if you own or co-own the vehicle I don't see any issues with attaching the GPS. I used the Zoombak tracker and successfully entered the tracking data into evidence during court. I'd recommend getting a model with a battery attachment if you can so you don't have to remove it frequently to recharge it.
[use according to your jurisdiction and situation]
I use Apple iCloud to track the nj/stbx on her iPhone. The court ordered me to continue paying for the phone service on the iPhone I bought her. I guess her attorney and the court didn't realize they were ordering me to look at the bill each month and see what phone numbers she's been dialing.
Haven't found anything exciting about nj/stbx by checking in on her location(s) or the dialed calls on the phone bill. I remain hopefull that nj/stbx will find another meal ticket to refocus her attention away from custody and equitable distribution issues.
It's been useful to know if nj/stbx is driving to pick up S8 before I do from school.
My nj/stbx cost me around USD 8,000 per fornication session.
My nj/stbx had this in mind (and still does) for me: the manipulated man by Esther Vilar