I have inadvertently ran my spindle for 5 mins or so (a couple of times!) without coolant. After I figured out what I was doing, I felt the spindle and it was warm, but just.
I have a cheap pump - probably $10 worth, and it was essentially quiet for the first few weeks - just a nice humming sound. Then it developed a really irritating noise - but still pumps the same. Anyways, I took to unplugging the pump when I wasn’t machining anything as the noise drove me batty. That’s why I forgot to start it a couple of times.
I’ve built a simple arduino based flow indicator that displays the flow rate and coolant temp. It will also start and stop the pump on a signal from the VFD (haven’t got that bit working yet - as I need to repackage the whole thing in a decent box first).
You can just start and stop the pump via the VFD - but I like to complicate things and have lots of readouts to look at - bells whistles and lights etc.