Pie,
I did a little searching the web and really could not come up with any specs for that converter. It's likely the original that came in the trailer, and has been discontinued. Which leads me to think it may be pretty old technology....in other words, it may not be multi stage.
One way you can test to find out would be to plug the trailer into shore power, and take a reading at the battery to see what the voltage is. If the charger is for instance, putting out let's say 13.6-14.2 volts, then that would likely be fairly normal. Now then, go back the next day, or several days later ( with it left plugged in to shore power the entire time ), and read the voltage again. If you are still seeing 13.6 to 14.2 or so, then there is a pretty good chance it's just a single stage charger ( this is assuming the battery is good, and has taken a charge correctly ).
But if you are now seeing around 13.2 or so, then it is likely a multi-stage, and has gone into a "float" mode. If you are seeing this 13.0 to 13.2 or so, then you are good and are in a nice comfortable maintenance mode.
There may be a label on the converter that shows what it's specs are.
You may want to consider replacing the converter with a new, modern one. Progressive Dynamics comes up often as a good brand.
Many modern travel trailers come with a china made WFCO converter/charger. Lots of folks talk trash about them, but truthfully, there are probably hundreds of thousands of them in service that are working fine. So you can decide for yourself whether all the trash talk about that brand is valid or not. So far, my WFCO is working fine, going on 5 years.
But if I were going to replace it, I would buy a PD, if for no other reason than it's made in USA, and it has a good reputation.
....hope this helps.