Does the motor on condonsate box supposed to run all the time

If it is pumping water all the time, yes. If not pumping, no, the float is stuck or the microswitch is bad.

Mine stopped working and someone said 'kick it to maybe free the float,' but that didn't start it, so I had a eureka moment and ran a very long tube across my cellar to a big plastic bin next to a sink. I go down there every 2 weeks with a bucket and empty most of it into the sink.

Cost me nothing, and saves on my electric usage. (Just be careful; it's acidic.)

Condensate pumps go bad fairly frequently since they are built cheap. You could drop the end of the tube in a bucket or just buy a new pump.
https://www.zoro.com/little-giant-pu...A&gclsrc=aw.ds