Troubles with Turn Signals 67 Barracuda

You may have some wiring melted in harness and causing strange "cross connects." This is hard to run down, without just pulling the harness out for access and unwrapping it and inspecting it.

You have an evidence of "meltage?" Smell? Appearance, IE plastic damaged on the harness wrap, etc?

There is absolutely NOTHING that should cause the flasher to react. It comes (sourced) from the fuse panel, on the key "on" buss, through the flasher, and goes TO the column turn switch. With the switch centered, it should be "open." IT is possible you have something crazy in the switch.
When it popped I was cruising at about 30 mph without the turn signal actuated. Since I've owned the car the radio has never worked and don't believe it's connected. The part that was odd is that the car hesitated and almost stalled for about three seconds after the pop, like there wasn't enough juice for the ignition and what was concerning is I'd think a fuse would blow before that would happen! No smell at at that indicates a burning wire or an electrical fire which I was absolutely concerned about. Nothing obvious either glancing. So in your opinion is it time to perhaps take the radio out and get the best possible view of the wires and unwrap any harness? What else makes it weird is this happened after about 15 minutes, not immediately. I should also mention my AutoMeter tach is connected to the fuse but still functions normally. Once again, the fuse didn't blow out which is so odd. Tach didn't blow out either.
I bought two more flashers from Napa but am hesitant to drive it as I don't want to stall out if it pops or start a fire.