what do you mean internal wiring ? where the wire came from motor/switch ?
From the original post the internal wiring refers to the connections inside the motor housing for reversing and the external wiring refers to the power cord's three wires coming
into the same location.
Since the woodworker wants to be able to reverse the motor then he will require some
additional external wiring to his remote switch
The white and orange wires are connected the same regardless of direction,
pins 1 and 4, and the black and red are switched between pins 1 and 4 to reverse the motor.
The red and black need to be connected/extended to the switch as per earlier suggestions and then the wipers of said switch need to be returned to pins 1 and 4.
If it is stalling/ hesitating then the wiring is most likely not tight/good connections, the switch is flaky with a bad internal connection or the switch cannot handle the current load and and its contacts are heating up causing a high resistance.
The full current draw of the motor, either from the start or run windings or both need to be addressed. The switch must have a current rating equal to the motor ratings.
What is the ratings on the switch you are using?
You say the motor is 1/2 hp. What does the motor plate ratings say?
Running hp/current is far inferior to peak/starting current.
cheers
EDIT:Too long typing and didn't see your post or on1aag's.
Do his tests and then respond to my two questions if you like.