That's it............

It no longer condenses.

Are your points arcing? That's it's function, to prevent the points from arcing. Unless it's shorted out then it prevents the points from doing anything.

Car won't start, with no spark or if it dies once it gets hot, again with no spark. Back in the day we always carried a spare condenser or two because failure was very common. First thing to do when your car woudn't start was to change the condenser. And that was when we had quality replacement parts. The points ignition was very reliable but the condenser was the weak link.

Or the one on the gauge clusters?

No matter where the cap is, it stops arcing or other noise. To trouble shoot, just disconnect it. If it is for the points, the car will then start if it was bad and you took it out of the circuit. Get a new one and put it in. It will run okay without it but pitting of the points will start so do not do it keep it out of the circuit long. If it is the dash capacitor, just replace it and be done with it. Capacitors only fail one of two ways: it shorts out and carries whatever it is hooked to straight to ground. On points the car won't start. The second, the capacitor "Leaks" which means it no longer works as a capacitor and does not filter noise. You will hear its effect in your AM radio when that happens. And it also leads to one side of the points to pit and the other to build up metal throwing your dwell off.

Using a ohm meter from the input lead to the case should tell you if it is open or grounded If it is grounded internally I think it is bad
I'm thinking it should be open and you can charge them with two leads, ! + and 1- from your car battery and the very carefully discharge it with the lead by grounding it to the case, it should arc
Don't become the conductor, it will shock you and hurt too

It IS the dizzy condensor. The main point (couldn't resist), is how will the engine run? My engine will start easily, idle well, and cruise at lower speeds smoothly. When I put my foot into it, it bucks and hesitates almost as if I had a rev limiter. And yes I checked the float levels on the carb.

I've had them start the engine just fine but the capacitor went intermittent, and the car would start shooting ducks. Thought I'd blow the mufflers apart in my Charger last time it happened.

Just because something starts and runs, doesn't mean the capacitor is 100%. Caps can (and do) break internally in such a way as go intermittent, and will drive a person crazy finding the problem.

I've had a couple capacitors go intermittent in guitar amps too.

Infuriating and difficult to find the source of the problem when that happens.

A person is actually fortunate when something completely fails, at least that makes it more obvious when the solution is found.

If the engine starts easily, idles well, and cruises well, I doubt it's the condenser. But it does sound like you have a weak ignition system. WOT puts more load on the ignition system and if there are problems, that's when you'll see them. But I could be wrong, been wrong before.

Check your spark plug wires for high resistance on the ends, ohm test them while moving the wires around, if they vary any at all replace the ends or the wires