There may be markings on the contactor. With the wires disconnected the contacts will be open circuit, the coil will show some resistance, but I wouldn't like to say how much.
Ok, I've changed the black wire from the limit switch to match @carbon 's amended drawing, and replaced the fuse he mentions with a 3A spade connector type as I dont have any of the original ones (it was 2A) and as soon as I turn the main switch on the fuse blows. I have also bridged the 3 indicator lamps to complete that part of the circuit too.
Agree if wired as amended dwg then shorting lamps will cause short and fuse to blow, they are no longer in series and links need removing, do that and try again chris
I'm in the process of re-drawing the diagram as a circuit diagram, rather than the wiring diagram you already have. This should make it easier to see how the thing actually works.
The switch top left turns power on to the saw, transformer is live.
Pushing the start button connects power from terminal 13 on contactor to terminal B. Once contactor pulls in power then flows through the contacts between terminals 13 & 14 to B holding the contactor in.
Pushing either the emergency stop button or the limit switch breaks the circuit stopping the saw.
Also main motor overload will break the circuit in an overload event.
As the coolant pump is connected after the contactor it can only be on when the saw is running.
This is how it should be - but I don't think this tallies with the last wiring diagram. I haven't put the other bits of the circuit in yet, but this should get it going. I don't see the point of using the NN contacts on the main switch to switch the indicator bulb on the transformer secondary.