You say that you can send it into a cycle, true?

There are two ways of having the unit clean at a different time other than the 2am, one is to have it live 12 hours ahead or behind either way works or the other is the back out the set screw and set with the gray rear pointer what time it cleans while having it on the current time of day.

Now if there is nothing wrong with the float, the injector is clean .. and there is no water going to the drain while it is in service, there remains only 2 reasons, either it is NOT cycling or the brine piston assembly/piston is in need of either work or replacement.

Now your system is neither straight day nor meter, as it has the red button and the elect with it might be missing the system up so that it is not really cycling like it should.