FA51-00 timer is used as an attic fan timer and is 40 yrs old. timer does not shut off.

SOURCE: I am trying to replace

The timer is wired differently than the old spring-loaded timer.
This is because the timer has an electronic clock instead of a spring.
The electronic clock needs power just like an alarm clock.
The white wire powers the clock.

Here's the wiring.
Black-timer wire connects to Hot-wire-from-breaker
Red-timer connects to Load (attic fan)
White-timer connects to white Neutral
In absence of a Neutral, connect white-timer to bare ground.

If you have your black-timer and red-timer wires reversed, it might cause the symptoms you describe.
Simply reverse the black-timer and red-timer.

If you want to test your wires to make certain:
Remove timer.
Separate wires for testing.
Turn on power.
Use ordinary tester.
Tape tester leads to wood sticks to keep hands away.
Power is ON.
Test each wire to bare ground wire.
When tester lights up, that is hot-wire-from-breaker.
Now test hot-wire to each of the other wires (except ground)
When tester lights up, that is Neutral
Not every switch box will has a Neutral
In that case white-timer connects to ground