Assuming that the battery is good, I suspect that you replaced a defective alternator with another defective alternator. If there is no external regulator the alternator is housing the regulator.
External regulators are normally shaped like a small box maybe 3" x 2 1/2" and about 2 1/2" tall. They are usually black or possibly blue on an old Ford. Follow the wires from the alternator back into the harness and see if it leads you to a similar box.
Defective alternators right out of the box is not uncommon.....annoying but not uncommon. If you have no external regulator, bring the alternator back and ask for another.
Jay in MA
I am working on my gf's 1965 ford falcon ranchero. The alternator went and I replaced it with a new one. I learned that there is no belt tensioner like my 98 corolla. The alternator is the belt tensioner. Anyhow, when the ranchero is running, all the lights are flickering from bright to dim to bright like somebody is playing with a potentiometer. Any idea as to why this would happen? There is no voltage regulator.
What is a voltage regulator and how is it fixated under the hood?