need to identify alarm manufacturer

I bought a used 2005 Toyota Corolla CE Automatic; crank up windows, (bare bones car) with an alarm installed. I did not receive any remotes with the car. There must have been issues with the installed alarm because someone cut the wire running to the installed horn/siren mounted in the engine compartment. The alarm activates every time a door is opened like it is supposed to and the only way to stop it is to start the car. The alarm flashes the parking lights and instrument lights. I can start and run the car ok otherwise. The alarm stops cycling within 10 seconds or so after starting the car.

The car was originally sold in California and moved to Nevada. It now lives in New York.

I am trying to identify the unit so I can get some information for it. I found it behind the small glove door on the left side of the dashboard. The sticker on it says Rooster. There are no other markings on the unit with a bar code or model number, just Rooster. I could not find a valet switch to shut it off. I figured someone on this forum may have installed one of these and can point me in the right direction. Any help is much appreciated.