Glad you've managed to figure it out Virgil, and I was assuming that the timer is a mechanical type as well.

Don,
I don't see how a pneumatic relay of the type you described would work in this circuit. If you installed one in which the time delay didn't start until after power is removed, then the first operation of a limit switch would just lock up the relay and stop the motor from running until the whole lot was switched off and back on.

As soon as a limit switch closes, you have power on the relay and timer. The relay N/O contacts latch it on via the timer N/C contacts, after which the limit switch opening again can have no effect.

Other than switching off, the only way for power to be removed from the relay (and thus the timer) at that time is for the timer's N/C contacts to open after the appropriate delay. The timing cycle has to start when power is applied to the timer (whatever type it is), otherwise it just won't work.