BOY !
You do things the hard way !
The wires to the cigarette lighter are common to the wires in the glove box light, you could have tapped in there much more easily .......
pop the light out, hookup, pop the light back in, just sayin .....

( I hooked up a female cigarette lighter socket to the glove box light and plugged my Garmin GPS in. Didn't need to modify the OEM Garmin plug that way, and all is hidden inside the dash )