Your 2013 24FBS is equipped with a Power Distribution Panel where all of the 120VAC circuit breakers and ATC 12VDC fuses are located. In the bottom compartment of this panel should be your CONVERTER that should keep your battery charged when plugged into shore power.
This google photo may show your Power Distribution Panel near the floor under your fridge. The CONVERTER MODULE in this unit will keep your battery charged.
You should be able to plug your 30AMP Trailler into a garage 120VAC 15AMP receptacle using a RV30A-15A Adapter (WALMART). If you need to use an extension to reach your parked trailer I would not go smaller than a 12GAUGE (12-3) heavy duty extension cord.
If your converter is a single mode 13.6VDC type charger thenyou will need to start checking your battery fluid levels at least every two weeks when plugged in. The constant 13.6VDC is right on the edge of boiling out your battery fluids which will do harm to the battery. If you have the SMART MODE Converter/charger then it should take care of your battery automatically. Post brand and model of your installed converter. You may need to upgrade it to a smart mode unit. I think most new trailer now come oout with smart mode converter/charger units.
We keep our two trailers plugged in all the time here connected to two separate 120VAC circuit receptacles in the garage.