Thanks guys. I got around to replacing the bulb today and it was as simple as I'd hoped.
Unfortunately, the new bulb hasn't fixed the problem. The old bulb was definitely blown, all black and what not. But I'm still getting the fast right turn signal and the new bulb isn't lighting up.
I guess maybe the socket went bad too? I looked into it, and there was some minor discoloration, kindof a reddish color, but nothing that screamed "bad socket" at least not to an auto ignoramo like me.
There was a small amount of water in the light housing, not sure how it got in there, but it's kept the plastic fogged up since I bought the car 2.5 years ago. Maybe the humidity did a number on the socket? The right blinker compartment had most of the water in it, as it's down on the bottom right side of the housing. No other lights have gone bad though.
It looks like I may have to have the mechanic fix the socket when I bring it in. I don't know anything about replacing electric components.
Probably a silly question, but is there maybe something I have to do to reset the bad light indicator (fast blinking)? Am I likely to have the new bulb blow if I leave it in a bad socket? Not sure if there's other things I can try in order to save a bit on the repairs bill.
Ugh, why couldn't have been a simple bulb replacement.