Should this Grasslin UWZ48-L hour counter in my septic pump box be rolling or ticking over?
That is an hours meter, it is not a timer.  (The Omron device next to it is a timer, capable of various modes of operation depending how it's installed.)  The hours meter is like the odometer on a car.  

The display is hours to two decimal points.  If it is working properly it should be ticking every .01 hours, or 36 seconds, when the load runs - probably the pump motor.  

If the tank is alarming and it's not moving, that indicates the motor isn't running or maybe short cycling, so there's a problem - couldn't say what.  

This time of year (summer here) my first guess is heat, maybe the overloads for the pump motor were preventing it from running during the heat of the day but came back online when things cooled at night.  But that's just a guess.