The pumps shut off when they sense they have reach the correct pressure (5psi)
The light is controlled by the computer which uses a sensor (electronics switch) in the diff to tell if the locker is locked or unlocked.
If the light blinks than it means your locker isnt locked, malfunction in the locking system, or the sensor in the diff is bad, or the wirring/computer is bad.
I had a sensor go bad in mine and the locker was working, I could hear the pumps shut off and I could tell the locker was working as I tested it offroad. But the locker light would just keep blinking, Unfortunately to replace the sensor in the diff you have to pull the carrier which can be alot of labor.
Hope that helps.