Hi Kevin,
If you want to try to identify the the wires to the motor nere is how to go about it.
FIRST UNPLUG THE LATHE FROM THE MAINS.
Set the reversing switch to the middle off position.
Disconnect one of the wires that is connected to the motor in the motor connection box. (This is to avoid the winding resistance from confusing your readings as it will only be about 5 ohms.)
Confirm that there is only one wire connected to terminal 2 on the reversing switch. Use your meter to identify which wire this is in the motor connection box and label this "A"
Confirm that there is only one wire connected to terminal 10 on the reversing switch. Use your meter to identify which wire this is in the motor connection box and label this "B"
Confirm that terminals 4 and 6 are linked together on the reversing switch and there is only one other wire connected to this point.. Use your meter to identify which wire this is in the motor connection box and label this "C"
Confirm that terminals 8 and 12 are linked together on the reversing switch and there is only one other wire connected to this point.. Use your meter to identify which wire this is in the motor connection box and label this "D"
Confirm that terminals 1, 3 and 7 are linked together on the reversing switch and there is only one other wire connected to this point.. I expect this to be live or neutral of the wire from the mains plug. Make a note of which one it is.
Confirm that terminals 5, 9 and 11 are linked together on the reversing switch and there is only one other wire connected to this point.. I expect this to be live or neutral of the wire from the mains plug. Make a note of which one it is.
When you have done this report the results particularly any difference to what I expected.
Les.