Amperage is dependent on the draw of the total of the brake magnets and associated wiring. Voltage to the brakes is controlled by the P3. Your battery condition will have little to do with brake controlling as the vehicle's alternator will be delivering power to the P3 and back to the trailer's brake system.
Tekonsha advises an initial voltage of 6 V and adjusting up or down from there. An improvement in electrical efficiency for the trailer's brake system can be had by wiring the trailer braking in a star configuration rather than a daisy chain, as most trailers are OEM wired. This helps to deliver more power to the brakes. An increase in wire size accompanying the star configuration will also help with maximum electrical efficiency.