The timer motor doesn't appear to run though I have jumped power to it and I could hear it running with power applied directly.
I am not sure what you did here.
I also checked by jumping directly from L1-black to orange with no reaction from motor.(extra spade to spade connector)
This will not start the motor.
The orange is not connected to the motor windings when the motor is at rest.
When at rest purple (connector 2 to B and A) connects in the run and aux (start) windings.
When the motor gets close to operating speed the centrifugal switch activates (connector 3 to 2/B) the aux winding is disconnected and the run winding remains connected.
This is done because if the aux winding is left in circuit the motor will overheat.
... as I recall, white, orange, & purple are the run circuits, green/ground, the other wires are for centrifugal switching of heating elements & timer.
White is Neutral. On a 3 wire hook up this is also green/earth ground.
Orange is the run winding. It has 2 purposes . First it disconnects the aux (start) winding. Second it provides a parallel circuit path around the push to start switch. This lets you release the push to start and the unit motor keeps running.
The timer is not really switched in by the centrifugal switches.
The centrifugal switch in the lower right of the wiring diagram does switch in the heating element. This ensures that the element does not come on until there is air flow.
In auto modes the timer motor does get power through the heating coil when the coil is shut off so in a way the switch does effect the timer motor.
In timed dry mode the timer motor gets power direct from Neutral through timer contacts (B/TM) to L1.