I had an '02 Camry for which I added a third party alarm to. The installer programmed it so the OEM remote controlled the alarm. Even the panic button worked (
horn AND siren would sound). Mine had a 'valet' bypass button high out of sight on the driver's kick panel. Don't think they would put a switch like that in the fuse box.
What happens if you open the door with a key instead of the remote? On my '02 the alarm would sound if I used the key instead of remote. Or... with the driver's side window down, lock the car and reach in and open the door with inside handle. Your car should alarm for sure then.
Hope this helps.