The voltage regulator in older Mustangs is a mechanical device that can be adjusted. See the Shop Manual for detailed instructions (in the 1965 manual, it is indexed under "Alternator Regulator"). You may want to replace this with a modern solid state, electronic regulator, but don't throw away or destroy the old one if you harbor any thoughts about showing your car. Points may be deducted if you don't have the original (or one that looks like it).
One strategy used by some experienced in the concours world is to use the electronic regulator when driving but swap it out for the original once you reach the show.
If you don't have the original and want the look, whether for show or other reasons, try www.amkproducts.com
If fixing/replacing the regulator doesn't cure your flicker problem, it may be your headlight switch in the dash.
Dash lights get power through a potentiometer in the headlight switch.
One end of this potentiometer consists of a coiled spring-like resistor twisted into a circle; the other part is a copper tab attached to the shaft of the switch.
As you rotate the switch in the dash, this tab is dragged over the coil, and more or less voltage is made available to the dash lights. After many years of service, the copper tab and coiled resistor can loose some of their shape and tension, so that the tab and coil do not always maintain correct contact.
The fix is to replace the switch. This requires depressing a locking button on the switch housing behind the dash (takes small fingers or a screwdriver used as a lever, and careful determination), pulling the switch knob out of the switch, then loosening the switch bevel with a large screw driver (there is a slot built in to the bevel; it will be revealed when you remove the knob).
submitted by 65Ragtop