Contact grease or WD-40 - that's what'll save you here. I used to struggle with stuff like this on my car too, until I figured out that connector oxidation is fixed with chemistry, not mechanics. Just disconnect the connector, apply some grease or spray WD-40, let it soak for a couple minutes, wipe it off with a rag and plug it back in. The main thing is make sure the contacts are completely fine and fit snugly into the socket.
You guys are right about oxidation, but I'd add - if you're gonna clean it with sandpaper, then definitely treat it with a protective coating after, or it'll just oxidize again in a month or two. That happened to me - cleaned everything properly, then August rolled around with higher humidity - green corrosion again. Now I either coat it with paste or just use alcohol + protective spray. And yeah, check the bulb itself - if it keeps blowing when there's poor contact, the voltage spikes and it burns out faster.
You're right, you don't actually need to tear apart the whole trunk. It all comes down to this connector.