Con541; thank you for adding the model number. Just for your information, you're missing the last digit of the model number but that's okay.
The timer controls the pump out period. This means it should drain all the water out first. It can then sit there and continue to be in neutral drain cycle even though all the water has been pumped out. Once the timer times out, the timer must momentarily stop the motor after the pump out time for a short time. Once the timer advances and the motor starts again, this is when the gear case shifts into spin.. The water level pressure switch will not have anything to do with when it should spin. If the washer is in the neutral drain cycle, meaning it is not spinning yet and it's full of water but draining and you were to open and shut the lid or push the timer knob in to stop the motor and then lower the lid or pull the timer knob back out, the washer would begin spinning with a water in the tub. I hope this answers your question. I added an image below with additional information on the gear case operation.