Car dies when shift to forward or reverse

I have a 1966 Ford Mustang 2 + 2 (289 cu. in.) V8 with four barrel carburetor. It has more than 170K miles on it. It starts right away, but when I shift the automatic transmission to reverse or forward it dies out every time. I changed the fuel pump and the fuel filter, but the problem persists.
I would very much appreciate your advice or any suggestions I might pursue. I have had this car for almost 46 years now and I cannot bear to part with it.
Please help. I am 72 years old and on limited income.

It sounds like a timing issue to me. Do you have points? A dwell meter and Timing light? Do a proper tune up with dwell angle set appropriately, and timing within specs. I would love to be an old fart like you but for some odd reason I would love to help you get this car going if you are within 50 miles of zip code 60010 let me know.

A vacuum leak a likely cause. And the secondary throttle on that Holley 4bbl can hang open slightly and cause the problem. Also, the carburetor base gasket and spacer might be the problem. With the engine idling, spray carburetor cleaner down the rear venturi and around the base of the carburetor and listen for a pronounced increase in RPMs.