[Greg'66 5.0]

If the fuses are blowing immediately upon power-up, that would indicate that you have a hard short to ground. If you have a multimeter, you can troubleshoot without wasting as many fuses. Remove the bulbs from the light housings so that you don't get erroneous readings from measuring through the bulb filaments. If you have incandescent bulbs for the turn signal indicators in your instrument panel, you'll need to remove those as well. Measure the resistance from the load side of the fuse to a body ground - you shouldn't see any continuity. If you have close to 0 ohms, you've got a short to ground. Disconnect both front & rear light housings from the wiring harness by pulling the plugs near the light housings and repeat the measurement. If the ground goes away, plug the light housings in one by one and check the resistance after connecting each one. When the zero ohm measurement returns, you've found where the short is. If you still see zero ohms with all the light housings disconnected, the short is somewhere on the harness. Since the brake lights share the same wiring with the rear turn signals, your problem could be in the brake light circuit. The brake light circuit gets power from a different fuse, so if that fuse doesn't normally blow when you stop on the brake pedal, you can eliminate your rear light housings as a source of the ground. If the fuse doesn't blow with brake lights and only blows when you try to use the turn signals, the problem is probably with the front signals.

For what it's worth, I ran into a similar problem when I first wired up my car. I don't have a wiring diagram handy so I don't know the differences between '66 and '68, but one thing I found is that wiring colors on the front turn signal/parking lights don't follow conventional automotive wiring colors. My repro light housings had 3 wires - black, brown, and blue. The mistake I made was that I assumed the black wire was the ground - it's really the brown wire that is the ground. When I connected my parking light wire to the brown wire, I inadvertently created a dead short. Once I switched the wires to what they should be, the problem went away.

 

[Greg'66 5.0]

Disconnect the turn signal switch connector at the steering column and try it again. The wires running through the column can chafe and end up shorting to ground. I would disconnect whatever connectors I could and measure the resistance in each portion of the circuit. At some point you should find a ground on one side but not on the other. Check your harness routing carefully and make sure the harness isn't running over any sharp edges that could cause chafing.

The spike in current that you had could have caused problems if things weren't grounded correctly. Electricity will always try to find a path to ground, even if that means running backwards through other circuits and eventually finding a ground. Taillight/parking light/turn signal circuits are usually the worst since they share different portions of the circuits.