From everything your question and details say i would answer that no your gps and anti theft alert light are not enough to drain your battery.
Gps tracker draining car battery.
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There is a misconception that a tracking device is most often the reason for the drain on a vehicle s battery power and for the vehicle not starting.
These can easily be installed by connecting the wires to the car battery there will be instructions provided when you buy the tracker.
I say that assuming that everything else is working well within your electrical system.
You can buy one for rather cheap on ebay amazon etc.
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Hidden gps tracker for car is a helpful gps tracking device to recover stolen vehicle compared to normal real time gps tracking system.
The hidden gps tracker for car are mainly used for bank financed cars to avoid fraud or stolen.
About 20 years ago this might have been the case and as a result the conviction arose that if a vehicle was wheeled into a service centre the problem must lie with the tracking unit.
The type of tracker your after is a hardwired gps tracker.