I have a 1990 ES250.

The starter makes a repeated clicking noise when I try to start it.

I thought it was a bad starter so I bought a new starter and put it in and
its the same. Just repeated clicking, about a click every 1-2 seconds. After
a couple of clicks I turn the key back to the off position.

I took the battery out of my nissan, same group size, and installed it in
the lexus and still the same clicking.

The wiring looks ok, I will have to take a closer look.

Any ideas?

Does this car have a starter relay?

I took the original starter and bench tested it with a car battery. First I
just activated the solenoid, and it snaps / kicks out nice and hard. Then I
put power to the main starter terminal and then ran a wire to the solenoid,
the starter gear shot out and spun nice.

I guess I should check for voltage drops?

Thanks