I have an Inglis Citation washer (15 years or so) that stops midcycle.
The 15 minute cycle stops at the 6 minute mark but the timer keeps counting down to the rinse cycle. The rinse cycle does kick in and spins to completion.
I had the timer rebuilt but that was a waste of money.
Any help would be appreciated.

"The 15 minute cycle stops at the 6 minute mark but the timer keeps counting down to the rinse cycle. The rinse cycle does kick in and spins to completion"

So Im assuming you are supposed to have 6 more minutes of the previous cycle (wash?) and instad the washing machine just stops, but continues to count down.

If that's the case, then it sounds like everything is working, but for some reason, during those last six minutes the timer just doesn't send the voltage to where it needs to go.
I would try replacing the timer (not rebuilding it).