Welcome to the world of repair! Yep, it even can happen on the brand-new trailers like yours!
First, let's get the names right: I THINK you talk talking about your water heater
The furnace is what heats your trailer, the water heater, you guessed it: it only heats the water!
And as my brother likes to jump on me to say, it's not a HOT water heater, 'cause if the water was hot, why would we heat it! He's a character, that brother...
So, the other thing is, you don't ever have to take out the water heater to clean it; the only time is comes out is if you have to replace it.
What gets plugged with stuff is the tiny little nozzle that points into the large U-shaped tube in the bottom right that disappears into the tank. The much larger silver nozzle supplies fresh air and the tiny nozzle supplies gas.
Cleaning them is fussy: it's soooo small an aperture that you have to be really
careful. I just used brake fluid on mine this weekend past.
On my water heater there are two tiny tubes ritgh beside each other. The second one is a thermocouple. But your trailer being so new, I would be almost certain that you have a piezoelectric starter, and that system does not use a thermocouple.
Good luck, and hang in there, more knowledgeable help will surely show up soon!
Other more experienced folks will chime in and tell you if that's a good or bad idea.