Based on your sig you have a t5. The reverse light switch itself is located on the t5 case. There are typically only two connectors on the T5 (excluding vss), the lower one will be what you're after for reverse. There should be continuity between the leads only when you're in reverse, no other time. I personally have never seen a reverse switch go bad but it wouldn't surprise me. There are connectors in the drivers side kick panel where you can test the leads for continuity without having to jack the car up.
If there is continuity all the time then take the switch out and bench test it. If it fails then you know what to do, if it passes then somewhere (most likely inside the trans tunnel) the wires are shorted together....maybe burned on the exhaust?