I have a 1968 mercury cougar and I recently replaced the headlights and they still do not work. I was wondering what the next step will be to see what the problem would be. Another problem I have is my gas gauge is inop how do I check that.
Check for power at the switch. Then at the dimmer switch.
You can unplug the sender and briefly ground the sender wire and the gauge should go above full. Put the key in the accessory position. If that works it is your sender. You can get it rebuilt for $90 if it is a standard sender. Reproductions are cheap but not always accurate.
Checking the power would be the headlight switch at the dash and then where is the dimmer switch located. Do you know how to check the sequential lights
Where would I ground for the fuel sender
The dimmer switch is that round button on the floor next to the driver side kick panel.
The sender grounds through the tank. But I think you are asking where to ground the wire. The entire chassis of the vehicle is ground so you can’t miss. Might be best to use an alligator clip lead to the flange on the tank where the sender is installed.
There is a great book on automotive wiring that will make your life better.
https://www.amazon.com/Automotive-Wiring-Electrical-Systems-Workbench/dp/1932494871