[Peter Serio]

Two things I would search for, one there should be a 3 wire loom that exits out of each of the front turn signal lamps. Two of those wires are 12 volt power + wires, one is to turn on the marker lights and the other is 12 volts + to turn the TS blinker light(s) on. The last wire (one per each housing) is a ground wire. I would check those sockets as well as the ground wire on both sides. The ground wire runs over to the core support. On 66 and 67 GTOs it is very common for those turn signal housings to rust and fall apart from the inside out. Often one or both of those housings need replaced due to rust in the socket where the bulb plugs in. (Those TS housings will hold water when the gasket for the lens leaks.)

After that you need to check the ground wire underneath the dash, that wire is a black wire & it is attached to the back of the gauge housing.

The end of the ground wire looks like this:

Here is a pic of the ground wire from the 2 bulbs which light up your green turn signal arrows. If that ground is OK. Next you need to check the ground strap/brace at the back of the gauge housing. It's right beside where the speedometer cable attaches to the back of the speedometer.

I can post a photo of the ground bracket if you need me to.