Hi Matt - You will be able to leave your battery in the trailer all hooked up to it electrically when you use the Battery Tender. The one you reference in your link is one that will work with your gel-cell battery too.
The link says it comes with a "ring-terminal" connection that allows hookup to hard to reach batteries. If so, this is how I did mine. The ring terminals fit over the bolts that are attached to the battery terminals and then there is a quick disconnect plug that you can extend out from under the battery box cover. You plug the Battery Tender into this, and disconnect at the plug when you want to use the trailer. The ring terminal part stays connected to the battery.
If you have to buy the ring terminal part separately, it is this one: https://www.amazon.com/Battery-Tende...000NCOKZQ&th=1
. I actually think you DO have to buy it, but it is only about $10. One of the pictures in that link shows the quick disconnect plug that you will extend out of the battery box.
The Battery Tender is actually able to recharge a completely dead battery, but it does it very slowly. It is a lot like a "trickle charger" that you may have heard of, but it has a better charging algorithm that will not boil the battery if left on continuously.
The Battery Tender is the device I first used on infrequently used vehicles. I changed to a Battery Minder because it has a desulfating feature that I wanted. It is slightly more expensive. This is the one I have: https://www.amazon.com/BatteryMINDer...3d670b6bc&th=1
and it DOES come with the ring terminal part.