The "ultimate source" is the battery. When the sun is shining, your solar system produces a "charge voltage" to the battery and when you're plugged into shore power, the converter/power center produces that charge voltage.
If you place a voltmeter on any part of the circuit when either system is "charging the battery" you'll typically measure 13.6 VDC. THAT IS NOT BATTERY VOLTAGE, rather it is "charger voltage".
Disconnect the battery/batteries from the system, wait about 30 minutes and then measure the voltage output of the battery/batteries. It should be 12.5-12.6 VDC. If it reads anything less, suspect that your batteries are not holding a charge and take them somewhere to have them load tested.
With a measured voltage of 11.4 "at the bed motor", I'd first suspect the battery output. If, on the other hand, the battery output is above 12.5 VDC at other locations in the trailer, I'd suspect a bad ground or a loose connection in the affected circuit...
But the first step, IMO, is to verify that the battery/batteries are actually accepting a charge and maintaining it.
If you're using a hybrid 12 volt battery (marine/RV deep cycle) then they should not be discharged below 70%. That means you only have 30% of the battery capacity available for use. Discharge beyond that point and you risk damage to the battery plates, making them "increasingly damaged"...
True deep cycle batteries, such as golf cart batteries, can be discharged to the 50% level, which gives you about 20% more available power than a "hybrid battery"...
If the battery box/label has CCA on it with any number behind it, it's a "hybrid" battery not a "true deep cycle" battery.
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS