Well, I'll answer my own question, in case someone else runs into the same thing in the future.
I have a RM2190
refrigerator. I found a service manual online (then discovered we had the same one in the document center) which describes it as a "balanced flue tube". It looks like it is supposed to extend up from a round hole in the rectangular box which surrounds the burner, parallel to the flue tube, to end near the crossover tube. The manual makes mention that if the opening of the balanced flue tube is too close to the crossover tube, that flame outage could occur.
I know my
refrigerator seemed to work OK without it , but I'll likely try to reinstall it, and I'll post here if I find anything unusual or notable when I do. I also need to get a few screws as the entire refrigerant coil assembly with the burner attached is loose relative to the chassis of the
refrigerator. I'm guessing that the vibration from going down the road has shaken them and the balnced flue tube loose. I know that when I bought the trailer the tire on that side had been replaced by a spare because it had failed, and the one on the other side (which it had been towed on) showed severe signs of belt failure - the tread had separated, you could see the cords through the resulting fissures in the tread, and half of the tire had taken on the rounded profile of a motorcycle tire.
At least the thrashing didn't cause the refrigerant coils to fail.