I have a 68 Mustang straight 6 1 BBL carb, 3 speed manual.
Noticed the other day that when driving at constant speed that the car hesitates (like I am letting off and pressing down on the gas pedal). It accelerates just fine.
No RPM gauge in car. When ever it is a constant speed, through city streets doing 35 or on the highway doing 60.
So, being an old car - where are the most likely problems areas - fuel pump? Coil? improper point gap? vacuum?
Points would be the first thing I would check. It sounds like the ignition is breaking down i.e. not enough spark getting to the plugs. The next thing to check is the wires. If you have access to an ignition scope or a Kv meter it can make the diagnosis easier.
Pulling the plugs and inspecting them can give you more clues see my answer here for help on diagnosing based on the plugs
My guess is fuel, try running a can of fuel system cleaner through it. A good spray of carb cleaner wouldn't hurt either. I'm guessing you've got a gunked-up jet in the carb that isn't giving a good spray pattern. It could also be a sticking needle valve that's keeping your float bowl from working properly, but I'd expect you'd have a problem when trying to accelerate too if that were the case.
Sorry your answer is a bit vague, but I'll share some thoughts on the old Ford straight six. to begin with if there is a vacuum leak your engine idle will sound higher as your engine is getting more air feeding into the intake manifold! If it had an automatic, you would find it wants to stall when you put it in gear as the modulator needed for the trans would lose that vacuum. Spark plugs would be a rough idle and continued rough running if total failure of one plug, but some will fail at higher rpm only as they can't provide spark under load. I doubt either of these matches your issue. Now a carburetor! the basic design of our car's carbs is that a small pump forces a shot of extra gas into the intake upon any push of the gas pedal but only a shot more as the vacuum effect of a car draws your fuel in the rest the time. The more air flowing the more suction of the fuel and that shot more is to make a quicker response happen when acceleration is needed quickly. the part that pushes that extra fuel is called an accelerator pump. They are common failing issues with carbs. usuall mounts just under the throttle linkage below the carb on the drivers side of the engine. should be a small arm moving upward when you hand pull back the carb linkage and the engine need not be running to look for this. Lastly I didn't get into the distributer and points/timing as issues in that portion of your car involve lost general horsepower not acceleration issues and/or idle speeds etc. you find pinging or knocking most common issues with out of time though low octane fuel will cause this as well.
