Since you do not have full (12VDC) at either light, then there is a resistance issue somewhere in the circuit. The problem is locating it with these runs typically buried inside the wall structures of the RV.
I would start checking where I could access (plug, pigtail end, and light bulb socket) to clean and protect the connections. A joint might look good, but still have some resistive issue from corrosion or dirt. And be sure to check/clean the ground connections too at any point...this could be the result of a combination of connections with slight resistance.
Kim and Steve, Mustang LCDR (Ret), '07 Damon Outlaw #1193
I have seen gross intolerance shown in support of tolerance, Samuel Coleridge
WE LOVE OUR OUTLAW RV