Well, now at least we know it has a T5 chip in it.
The fact that a simple lf search yields zero results, leads me to think 2 things
Watchnet has their own proprietary system, this could be possible, or they could just be rebranding something else, but that should have shown up with lf search
or
The T5577 chip is blank, and there is also an HF chip inside the fob, and that is what they are using
Did you try TagInfo?
Can you pry the fob open to see inside?
Did you also try Amals suggestion above?
so next, 2 things