The worst part, is that the voltage sags way lower while travelling, and you will not even be getting 13v when going down the road. I agree this is and issue, and I have no idea what the solution is. Newer vehicles with their high tech charge management seem to exibit trailer power issues. Another example is that once towing, 14 volts is rarely seen, and only when coasting, and only with the cruise control off. You can monitor it through the engineering test mode.
2013 F150 XLT SCAB 4x4 w/3.73's, Rousch CAI, Resonator Bypass
Traded my excellent 2011 F150 - Vehicle #10, and the best I have owned.
2011 F150 SCAB 4X4 3.7 w/3.73's