Since the Security light is the factory light, I still don't think you have a problem with the Clifford system unless they tapped into that light instead of installing the Clifford LED.
Since your car has OBD-II diagnostics, have you tried pulling diagnostic codes, both active and pending? Maybe there is one tripped for an unrecognized key or similar. When I get some free time this weekend I'll try to find a wiring diagram of the Clifford so I can give you a bit more feedback on what you describe above. It's really up to the installer to chose a location for the starter interrupt relay. There should be a wire from the alarm module though labeled something like "starter interrupt." If you follow that wire, it should get you to the relay. Keep in mind the Clifford wiring diagram will be generic and not specific to your car.
-Rod