I always have a spray can of "electrical contact cleaner" (plastic safe) with me for just the kind of problem you're having. 12V systems need clean contacts without any contamination to disrupt the current flow. I can't possibly tell you how many times in my 30+ years of camping where the lights on a trailer or a towed vehicle didn't work and a liberal spray of this cleaner on both the male and the female connectors fixed the issue. Simple fix, try it!!!
Days camping (2015)----88 days
Days camping (2016) ---110 days
2016 Wildcat MAXX 28RKX (33' TT), 2007 13' Scamp
2015 Ram Laramie Hemi
30 years RV'ing
12 different RV's