I have not used the unilight system but have used other lighting and flight controllers with my Royal Pro and Profi Tx16 and had no issues with getting the features to work. Have you tested your Unilight with say a servo tester just to check that it does go off at max -ve travel.
Also have you checked on the Tx servo monitor that the Unilight channel is moving all the way.
Reading the Multilight instructions it should also be possible to use the multiswitch setup or fixed values and flight phases to get more than 3 switched display options.
