You dump the tanks when they are full. I wait for mine to be all the way full before I dump them. We have the black tank flush system installed on my 2009 Big Country 3490rb so that is not really a problem. I have always filled the gray tanks up as well when I flush black, that way I have plenty of soapy fresh water to rince the sewer hose with.
Your monitor will show you all the lights ON once you are full. Keep in mind, that even though the sensor turns the lights on, you still have more capacity to fill it up some more. Just don't let it get up to the level of the floor. That is too full.
If you flushing system does not empty it enough to turn the lights off after you dump, you might have some debris on the sensors in the tank. So flishing it out from the toilet might be in order. There are some pretty good wands that you can use that will allow you to get into the tank and flush it. I don't know the plumbing of your tank, but explore that if it's not showing empty all the way.
As a last resort, if you can't get it to empty on the monitor, and you still want to get it to work, and flushing did not help. You can fill your black tank about 3/4 full and then tow it around the town. Shaking up the contents of the black tank when you are towing, also risnes off the sensors and loosens up the stuff that is stuck.
Good luck and keep us posted on your progress....