Forgot to mention. 64 ½, Holly auto C4, air, power steering, points and condenser changed to electronics. Hot coil.

As for verifying if its a HiPo, there are a couple of differences.  The exhaust manifolds are considerably different.  The biggest difference is the solid lifter cam.  If it revs out easily past 5,500RPM its likely not a typical hydraulic cam 289.

MS wrote:

Post some pictures of the engine showing distributor, harmonic balancer and intake manifold front bolts where they go through the intake into the heads.
Pretty much, anybody that advertises a Mustang for sale with a 289 having a chrome air cleaner and a hipo decal called it a hipo 289, but very few are. The solid lifter cam would have needed many valve adjustments over a 20 year period. It might be one, but the odds are against it.
Post some pics and we’ll try to help figure out what you have.

Does it feel like a miss, or a fuel issue? Or maybe bad ujoint? Have you ever changed plug wires? Open the hood on a dark night and observe the plug wires. Old, rotten ones will show blue sparks all around them.

Agree with MS’s assessment, and post some pictures.
Another check to see if it has Hi-Po heads is to pull the valve covers, Hi-Po heads had screw-in rocker studs and a raised boss for the valve springs that is cast in the heads.  Note that screw-in studs could have replaced the press-in studs so this is not a slam dunk that they are Hi-Po heads.
As I remember, the Hi-Po block has screw-in plugs instead of press-in ‘freeze-out’ plugs.
 

 Looks like I should have given a bit more information so you would have more to go on and things make a bit more sense knowing a bit more of my situation. I have not put many miles on this car. I worked at the same place for 30 year which was 2 miles from my house and for the last 8 years I have been retired. I have 4 Classic/Antique cars I try to keep on the road. So, do the math and there are not a lot of miles to go around.
Anyway, my wife told me about the Mustang through a friend. It was a true ‘barn’ find. The wife got it during a divorce. Didn’t want it, wanted to piss off the husband. Parked it for 15 years until she decided it was time to let it go. Although it was hit at one time the body was clean, the other parts, not so much. Engine was supposedly rebuilt so I changed everything else, springs, shocks, lines, brake parts, trans rebuilt, flywheel, water pump, air conditioning, radiator, added power steering, new wiring, I probably touched every bolt and screw on the car by this time.
Past month new wires and plugs. Now back to the problem. When I had the trans rebuilt there was the vibration and the mechanic said a tooth was missing on the flywheel and that was the cause. He put a new one on and I didn’t notice a difference so I made him change it out for another one and again no difference. Has it gotten worse, I think it has. I would have though the harmonic balancer also but from what I could research the vibration should get worse the faster/higher the rpm and in my case the engine smooths out. I use to be able to keep my idle around 800-900 but unless the car is completely warmed up it will stall out as soon as I try to move it. If I set it a bit above that it does not and also idles smoother. Sorry for the long response, I know some of you are not retired and have better things to do although I do appreciate the help and insight given. I’ll deal with the HyPo thing later.
Thanks again,
Randy

You might try checking the spark plug wiring for ‘cross-talk, and the distributor cap and rotor.  Also, make sure you are not mixing 28oz and 50oz small block parts.

New(er) camshaft has a different firing order than old 289s
Cam been changed?
6sally6

If you block the PVC you will have oil spewing out of somewhere.  You must vent the crankcase.

There are sources of vacuum leaks that you need to consider beyond hoses.  The carb base gasket, the intake leaking into the lifter valley, and possibly even a valve that isn't sealing properly.
 

So, it looks like I have a regular 1966,  289 in my 64 1/2.