That'll do it. If the power supply output can't keep up, it may click on and off.

Could be yeah. Not sure what the cause is though. Usually I'd say bad connection, and I don't have experience with these to know how the power regulation circuit is designed. It's possible with dc-dc converters that low PSU voltage could cause over-current which could have caused the connector to melt like that. That is unless there is a component that let out the smoke right near that connector I cant see?

I don't see anything in particular that would indicate something let out smoke. This happened overnight so I don't really know exactly when it happened or why or how. Took off the heat sink and I don't see the sign of anything else burnt out either.