Need some advice...

My home was built in 1908, started a bathroom remodel months ago.
I'm trying to install a GFCI that will turn the bathroom lights on and off. The GFCI comes with a light switch and a electrical plug in. Just trying to get the lights working the way they were before this project began.

I have 4 wires, 3 are black and one is vanilla colored. I bought a no contact voltage detector, there's one hot wire and it's black.
The lights are on both sides of the medicine cabinet, and when I checked the wiring for voltage where one of the lights goes, there's no dectection of power.

The GFCI has 4 screws- 2 on top and two on bottom and then the ground underneath. I have tried every possible connection except for the correct one to get the light switch to turn the lights on or off. I've been able to get the lights to work if I manually turn them on with the on/off switch on the light itself, not from the GFCI.
Right now the GFCI is wired with the hot wire and the vanilla colored wire wired together around the brass top screw, the remaining two black wires are wound around the silver screw on the other side on top. The two wires( Switch leads) that came with the GFCI are threaded into the bottom of the GFCI into the holes by the bottom screws.
It's not grounded yet. But the lights work manually and I have electricity in the electrical plug.

What am I doing wrong that I can't get the switch to turn the lights on and off?

Thanks for any advise you can give.....

Ms Jen.