Is there a sewage cleanout in your yard? There should be one if your house was built after
1960. It is normally used only if you have the roto-rooter guy out to get roots or other blockages out of the waste line. It is perfectly fine to dump your tanks into this outlet using your slinky.
As for the tank monitors, they are on the outside of the tank, and might have come loose. I don't know what kind of glue or tape you would need to restick them, but that is a google away. Of course the wires at the monitor itself might be loose - and you don't have to crawl under the Airstream to check behind the monitor panel.