Yep dielectric grease for sure. I fill the connectors with it and haven't had any issues since!

 

Yep definitely use the dielectric grease. I use it a lot on my motorcycle which has a lot of wiring exposed to a fair amount of rain since I ride in all weather. A tip though is to always wear latex gloves when dealing with it. Once it gets on your hands it has a tendency to want to get everywhere.