I've seen that problem on both connectors of one of our two 940's. A P.O. may or may not have used high intensity bulbs (higher wattage) and half-melted the connector and/or improperly seated the contacts when changing bulbs. When a replacement bulb is pushed onto a slightly damaged connector (with loose contacts) it doesn't take much to have the bulb contact spades go down the side of the connector contacts rather than into the middle of it. You'll then get a poor connection, dim lights, heat build-up and the connector will really start to melt around the contacts. The only good solution is to hack off the old one and splice in a good used one. Do a proper wiring splice (heat shrink tubing over a proper crimp or solder splice) as this is a mildly high amperage circuit and is exposed to the elements. If you have a choice, get a used one from the same side so the wire colors will match.
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Dave -940's, prev 740/240/140/120 Never overestimate what little I know.