The trucks alternator and charging voltage will be mostly determined by the trucks battery. If it drops to say 13.6V then there is less voltage difference to charge the trailer battery. The low voltage involved means that you need bigger wire.
Sure you can calculate the voltage drop of the wire but there are other factors including the batteries and truck wiring. Can you connect directly form the truck battery to the trailer battery? ie The shortest possible distance.
I would beg, borrow or steal (not really) a cord or other wiring and try it. Even if the trailer charging is limited you might get enough amps to allow usage of the trailer while maintaining the battery.
