Assuming it is properly wired FROM THE FACTORY.... Both the rooftop antenna and the park cable go either to a wall plate with a 12 volt outlet, Antenna connection, Light and switch or a "Box of many buttons" (matrix switch) Assuming from your post you have the wall plate.
NOW: possible issues.. If you get good TV reception with the switch and light ON even if the antenna is down.. Odds are it is properly wired.. Does signal strength go down or away when you turn off the switch: Yes GOOD, No Bad
now with the switch OFF it should .. Pick up cable
You will have to re-scan the TV (Menu setup channel scan is one sample path, there are other paths depending on TV)
First possible issue:.... Did a prior owner "re-task" the park cable for Sat-TV? If so you may have to restore the connection (Should be the center port on the back side of that switch)
Second: Cable issues (I now have that, am working on it but I almost never use park cable so.. Who cares)
Third: Cable system: Some cable providers have gone all encrypted digital. Your TV will NOT get a usable signal without a "Set Top Box" to translate and decode.. My feelings on this border on political so I won't go into them.. But this is a common.. I can not name the systems but the park office can tell you if THAT is the tribble.