once my car is off (key is out), everything still functions (air conditioning, fan, radio, etc etc) and my anti-theft light flashes like crazy (like 50 times faster)

i didn't think it was much of a problem until recently my battery kept dying and i've had to jump start my car after not using it for a few days. i have a 1996 gsr, anyone know what the problem is? this might have been covered before but the search function isn't working right now.

 

Faulty ignition switch perhaps.