You and I have the same model year, though different models.
The thin wire with the plastic rectangular thing on the end is a temperature sensor. If the batteries get hot from over-charging, that sensor will shut off the charging system. Tape the plastic thing in between the batteries, to one of them, in the middle. With the batteries pressed together, the temp sensor monitors both.
There is a lot of discussion on batteries in other forums. Some people say it's best to use two 6 volt batteries in series instead of two 12 volt batteries in parallel. Others say to buy gel filled batteries. Then there is a 3rd higher-tech dry cell. Costs can get up to $600 a pair. I contemplated my options, and decided last July to replace my original batteries with a pair of Walmart's yellow label Everstart Maxx Marine batteries for around $75 each. They are much larger than the originals with increased reserve capacity, but they still fit in the tray. The height fits too. it's a snug fit but still fine. I keep my receipt in the RV. If the Walmart batteries give me trouble, the solution is just a Walmart away. One thing I like about them are the deeper wells. You can fill them with distilled water until they touch those tubes, and you still have plenty of room to prevent over-boil. I also like the integrated carry handle.