You probably should determine if you have Electric Brakes or Hydraulic surge brakes. Having an installed battery and break-away cable probably tells you that Electric Brakes are installed. All of your SAFETY LIGHTS are powered by the Truck Battery when the trailer cable is hooked up.
Most utility trailers have the SURGE BRAKES as they do not require a BRAKE CONTROLLER in the truck to use them. Keep in mind that most states DOT have towing laws that stipulate that trailer brakes (separate from tow vehicle brakes) are mandatory when the trailer exceeds a certain weight limit.
ETRAILER is good place to buy parts and systems for all things trailers...
You should be able to charge your depleted 12V Battery using a 120VAC battery charger. When you connect your trailer cable to the truck you may be able to tap the truck 12VDC line and this would trickle charge your trailer battery when in use...
Your utility trailer battery should hold a charge for a long time when sitting as there will not be any parasitic drains to run down the battery.
My Posts are IMHO based on my experiences - Words in CAPS does not mean I am shouting
Roy - Carolyn
RETIRED DOAF/DON/DOD/CONTR RADIO TECH (42yrs)
K9PHT (Since 1957) 146.52M
2010 F150, 5.4,3:73 Gears,SCab
2008 Starcraft 14RT EU2000i GEN
2005 Flagstaff 8528RESS