I'll have to take a look at the wiring diagram for the SRS light. Since it doesn't flash out a Lamp Fault Code (LFC) you'll either need to get access to a professional scan tool that will access the SRS system or you can start by checking all fuses related to the SRS system. Maybe, just maybe, the lamp is configured such that a non-functioning, non-powered SRS module will trigger the SRS lamp and all it needs is to have a fuse replaced.
The light being on with no LFCs would NOT be an indication that the SRS system is working properly. Maybe people suggesting that think that because they connected a powertrain scan tool and did not get any codes. A standard consumer-grade scan tool will not be able to pull diagnostic codes for the SRS system.
-Rod