2001 Mitsubishi Galant: Would it be easy to install the bulb connector and the wiring?

My right headlight is dim. I changed the bulb thinking that might solve the problem, but it didn't. I noticed that the connectors are corroded due to heat (a common problem with Galants). I called the dealership, and they quoted me at a price of around $235 which I think is ridiculous for an hour or so of work. Would this be a job that I could do myself? What would it involve?