Hi Dave,
I sound that schematic as well. I was having trouble sorting out the contactor terminal designations. I’v now sorted it.
Note that the live and neutral identifications are swapped on that schematic.
IT appears the the Normally Open (NO) contacts on the contactor, or their connections are at fault.
From the older circuit:
Permanent live on the contactor Coil (A1)
Circuit from other side of coil (A2) to the (NO) Start switch (Right Hand 2).
When Start pressed circuit from Start (Right Hand 1) to E-stop , through guard switches and ON /OFF/Reverse switch (10,9) to Neutral.
We know all the above works because the lathe runs if Start switch is held. This is where it goes wrong . The Stop Switch which is normally closed (NC) des not make sense with a link from the Left hand 1 & 2 terminals. This circuit goes nowhere.
However if we link RH 1 to LH 2 (i.e. short brown wire across not up and down) it will work.
So when the contactor energises on pushing Start the NO contactor contacts (13NO & 14NO) close. This connects A2 throug the NC STOP switch through the repositioned link through the E-stop & guard circuit to neutral. When you press Stop this opens andcontactor drops out.
So the fix is move the short brown wire from the terminal with the other brown wire to terminal on the other side of the switch (at the Bottom in the picture) This may mean moring the brown wire from the contactor to the TOP terminal (currently with single brown wire) so the linking shorting brown wire can reach across the bottom of the switch. This connects a brown and blue wire to the same terminal which sounds wrong…
All the above assumes the start / Stop switch terminas are Start on one side and Stop on the other which is what is shown in the photo.

View on back of switch
Robert.