All M-codes require a "Finish" signal to let the control proceed to the next block. When the relay comes on for the coolant pump, there must be a set of contacts in the relay (or maybe a pressure switch) that will confirm that the coolant is on. That switch or relay will generate an "MFIN" (M funtion finish) signal to the control.
I would guess that your control has some "Ladder" logic in the programmable controller that will show the status of all these signals. See if you can find the "Ladder" display, or (better yet), some Ladder documentation from the machine tool builder.