Can you tell what color the wire is?
Another way you could do that is to use a "heavy" test lamp which will draw a lot of current. This is something I occasionally find handy.
I keep an old tail/ stop socket and bulb. This mess of old is INCREDIBLY handy. If you want it to draw little current, use the two wires and not the socket ground, placing the two bulb filaments in series.
If you want a little more draw, use the tail light wire (and socket ground), which is a lot more current than a typical 12V test lamp
If you want more yet, use the stop light wire and ground
And..........if you want more yet, wire both tail/ stop wires together, making both filaments work together.
Hope I didn't lose you
So.................Go down to the brake warning light switch, pull the wire off the switch and ground it. With the key on, the warning light should come on. This will confirm it actually works
Reinstall that wire, go in and grab your unidentified wire, and hook your "heavy" test lamp to it. Because your "heavy" test lamp draws a lot of juice, but will not hurt the circuit, it draws more current than the warning lamp bulb. This will cause the warning lamp to light, maybe dimly, but if you have a "live" wire there, your "heavy" light will not burn anything down.
(The other thing this junker of a test instrument is good for is charging small batteries, when your charger is "too big." You can configure the device several ways, as above, to adjust charging current to the (motorcycle, etc) battery.