The driver side front signal light on my wife's 2001 solara has a short. Would I be able to wire it the back signal light so that it can work?

 

Take note the front LH signal wire is connected to the rear LH signal wire at a junction box. This box is located way up under the passengers side of the dash on the right side of the center climate control system under the dash.

Are you sure it is the front LH wiring?

Did you check the socket and bulb for problems? Perhaps even pushing the wire out of the socket to make sure the end terminal is not touching metal then checking for a short?

The rear bulb has two filaments in one bulb, brake and turn signal. Check this bulb and socket for possible issues? Also check trunk wiring harness for damage.

If you just run a wire from the front LH socket to the turn signal switch and cut the original wire, the rear LH bulb will no longer work.

Assuming the issue is the front signal wiring. You need to find the junction connection and cut the wire going to the front LH bulb prior to the junction connection.

Front LH signal wire color is Green/Black. Note the turn signal switch has two Green/Black wires running to it. The other going turn signal flasher.