Meanie wrote:

A four lamp fixture with two ballasts will operate two lamps each.

I've looked this up last night, watching videos and googling how the things
work so I agree with you that it's 1 ballast for 2 lamps.

My ballast is so old, that it's made in the United States (NJ in fact). So
it's probably no longer sold since it's most likely "magnetorestrictive",
which means that it squeezes an iron core at 120 cycles per second (which is
causing the loud hum in one of the two ballasts).

Apparently there is no repair; it can only be replaced, but it can't be
found, so it has to be replaced with a different ballast, which may have to
be T8 because they may no longer even sell T12 ballasts.

One will control the outer lamps and the other will control the inner lamps.

Thanks for saying that one controls outer and one controls inner.
Is that the standard setup?

To determine what ballast controls what lamps, you need to follow a wire
to the tombstone (pin) connection of the lamp.

Yes. I saw videos where people followed those wires.
I like the name "tombstone", as it fits the rounded-top rectangular shape.

I also found out that a T12 is 12/8ths of an inch in diameter, so, just
looking at the lamps, I should have known that the diameter indicated a T12
while the diameter of the LEDs indicated a T8 (8/8ths of an inch), although
neither seems to be that large in diameter in actuality.

should indicate For example, follow the
yellow wire to one of the connectors. If it's the inner lamp, then that
ballast controls those two lamps and the other will control the outer two.

Yes. You are correct, in that I looked this up and these are the colors:
The ballast has 2 yellows that go to both prongs at one end of two lamps.
It has 2 reds that go to both prongs of the other end of the first one of
those two lamps, and then it has 2 blues that go to both prongs of the other
end of the second of those two lamps.

I think I just have to remove stuff to see where the ballasts go, but in
looking up how to replace them, I realized that I will never find a 1:1
replacement.

I think it may be "easier" and more cost effective to just replace the
entire assembly. Any suggestions for an inexpensive replacement?