Not a "hesitation" but more of a "stumble"...

[Just Carbs]

I doubt this distributor will work, as I have a 392. The distributor is in the rear of the block. Also, the heater box is still in place and would likely not allow for such a large aftermarket distributor to fit.

Your so right. My bad.
I was thinking 361 from another thread.

 

[Gregg Benedict]

This does sound like an ignition related issue.

Do you have an ohm meter you could use to test the ballast resistor? You could also get a new one. They're not real expensive and never a bad idea having a spare in your trunk if you plan to stay with your current setup.

I do have a spare new ballast resistor. However, it is for a 1968 Chrysler. Will that work?

 

[mgm1986]

That is a good question. A quick search on RockAuto suggests it would as they show the same parts for both 1958 and 1968 Imperial.

1958 CHRYSLER IMPERIAL 6.4L 392cid V8 Ballast Resistor | Shop Now at RockAuto

1968 CHRYSLER IMPERIAL 7.2L 440cid V8 Ballast Resistor | Shop Now at RockAuto

 

[jmustian]

So, after doing some work on my '58 Imperial, I'm getting a weird stumble at times when driving it. It's kind of hard to describe it. The car idles great, and also accelerates great from or stop or while kicking down the transmission in passing gear. However, occasionally it stumbles, mostly while flat cruising at speed. The stumble is seems like the engine looses power for just a split second, then immediately recovers. You can even feel it, like one of the cylinders missed. The other thing is, it doesn't always happen. One cruise, everything is fine. On a another, I might get 2-3 of these stumbles. I'm hoping some of you gurus out there might have some experience with this and what it might be. Unfortunately, I have a feeling it might be a myriad of things.

Things that were replaced: Spark plugs, spark plug wires, distributor cap and rotor.

It still is running on the points distributor, and that might be the problem, but I'm not sure. However, the points were recently cleaned up and adjusted. I want to go with an electronic ignition before the year is out. I also still use a generator.

Could be as simple as water in fuel.

 

[Gregg Benedict]

An update on this... So, I wanted to drive the car a few times to be totally sure, but I did solve the problem. I did check all the ignition wiring, which seemed good. Then I changed the ballast resistor. All the stumbling problems were solved. That was something I never experienced before. Usually when a ballast resistor goes out, the car simply dies and cannot be restart. In this case, the resistor looked fine, but there was obviously something wrong internally that was giving me an intermittent stumble. Another case of always trying the simple things first...

 

[mgm1986]

Awesome, love a simple and inexpensive fix!

I had the same type of issue last year, driving down the road at speed it would have an intermittent "stumble" or miss but otherwise ran fine. In my case I had a bad HEI module that was only a few months old. New module resolved the issue and now I keep a spare in the trunk just in case.

Enjoy your ride!