With the newer Rv, we get far less info to help with finding trouble and that leaves us guessing more and more.
Let me throw in some guesses and ask some questions and maybe we can get you started?
First question is to make sure you know the Rv well enough to not be missing a different switch for those lights? Easy thing to miss if new to the RV but I used to go on TV repair service calls and find the TV was not plugged in, so I'm paranoid on some obvious points???
But assuming that not true, do you have a meter to test for voltage and ground? That might be the next best way to go about this trouble. Part of the guessing is that LED can be wired so many different ways and I do not know what plan they may have used but will do the idea they use a "normal" way?
If you think of the four lights as being in a string or long row, 1 through 4 with 1 being the closest to the switch, I did this drawing of what I might try first.
Click this snip to get a better view!
What I'm calling "normal" is a guess on what they actually did on LED but this may be the best chance!
To make it work, they pick up 12V from some source, maybe right at the fuse or breaker, run to the first light and back to a ground which they pick u[p "someplace" that we don't get info on where.
But since there is one light working, we know for sure that it is not a fuse/breaker or ground loose. Assuming the switch does turn that one on/off to say it is god at the switch!
So the green path is what makes the first one work! What we don't know is WHERE the path to the rest is open/broken.
If no work has been done to cut wires or such, the odds are good that the circuit is open at the place where the wires from the first light meet the main wires, either the hot side or the ground side.
We start with the idea that wires don't usually break in the middle but at connections which come apart!
Where each light is connected, there are likely to be two wires from the fixture that go into the ceiling and if we pull on those two wires, we expect to find a connection where three wires come together.
In that connection there should be one wire from the light, one from the battery source and one going to the next light. I don't know what type of connector they may have used but things sometimes don't work like they should and one wire may have slipped out and not been connected solidly, so that after some shaking around it backed out far enough to lose contact!
I would first check the light number one as being closest to the switch??? Since we know it seems good and the light works, does the wire passing the hot and the one passing the ground on down the line seem solid?
Sorry ,if this is spelling out too many things you already knew! One of the problems with forums is we never know what the other person knows, so ignore any excess in my explanation.
Truth is that it may be far easier for me to talk about than for you to find!
I'm betting they are not all lined up in a neat row so you can tell which is 2 and which is 4!