>i.e. have search history for that exact tracker device or have testimony from a mechanic or technician who advised you on what the device is

I disagree this should even factor in. If they have not presented you with a warrant making clear they installed it, you don't know who installed the device. Knowing what the device is != knowing who installed it, their intent, or where the installer got it from. Nor do I think that a savvy criminal removing a tracker should become grounds for searching browsing history for parallel construction purposes since I somehow doubt third party records are answered in yes/no format, and the phrasing of query strings could be rather broad, leading to a reasonable request of search activity between the dates of installation and when they felt they "smelled a rat". In which could be bundled other incriminating evidence to spawn off new ledes.

If actually telling the person you as a government agency installed it invalidates it as an investigative technique, maybe it shouldn't be being used in the first place. Police shouldn't have to resort to breaking basic decorum routinely in doing their job. It's just converged on that because the population under observation aren't necessarily well equipped or educated sufficiently to be savvy on this sort of thing, or to make enough of a stink. Law enforcement also relies on law abiding people to remain silent on these matters because "it'll never happen to me" when there is no guarantee you won't become persona non grata one day.