Dielectric grease is great for protecting electrical contacts from corrosion and anti-seize. Its used widely in the auto and electrical wiring industry. You pack it into the mating connectors and housings. It really doesn't do much good on the outside of the housing, only attracting dust. Its effective at keeping contacts dry in outdoor or wet areas. It can make it easier to slip off things like spark plug boots after they have been connected for a long time. It reduces the chance for sparks and contains them, nice around combustible materials.
But it is probably not the best option for routine connect/disconnect application where there is exposure to dust which will stick to it and make a mess. You want something light enough to not attract dust, non-conductive, non-flammable, not damaging to paint or plastics. Silicon type sprays seems to be a go to for these types of applications.
As far as cleaning, use a contact or tuner type cleaner.