Have a strange miss.

I have a 73 Challenger 4-speed with a stock 360. Lately, it has developed a miss/backfire.

It doesnt do anything when accelerating. And it doesnt do anything when backing off. But after I let off the gas to back off, and then just touch the gas to start accelerating again, it stumbles and backfires (out the back). Once I give it gas, it smooths right out.

I've had the car for about 5 years, and it always ran good, so I never tuned it or replaced anything, although it would do this same thing on very rare occasions. But now it is doing it almost all of the time. Most of the time it is in storage, and doesnt get driven very often. I put fuel stabilizer in the tank and always use high test gas. I also use engine oil with sufficient ZDDP.

Does it sound like fuel or electrical? Time for a full tune-up? Timing need adjusted? Carb need rebuilt?

I'd like some opinions before I start replacing stuff.