Used auto parts are all but impossible to find, as far as I know, in King County these days. The Brightwater Sewage Treatment Plant in Woodinville used to be a sprawling salvage yard called Fitz's, that shut down suddenly about a decade ago.
I was told, and this may just be urban myth, but I heard it a number of times, that the owners of several local car dealers got together and bought Fitz's to shut it down and eliminate competition.
Last time I even tried to get parts for an old domestic rig in the greater Seattle area I went to Whitfield's off Highway 9 in Snohomish. That was easily a dozen years ago. A quick google search makes it look like they may not be in business anymore, but I drove by a month ago and there were still plenty of cars out there. Unsure if they are just rusting in the rain, or still part of an active salvage lot.
I do know that Gundies way up in Whatcom County is still going strong, and has just about everything you could ever want, but it's a hell of a drive from Seattle. They are the only functioning wrecking yard I know of still in operation in the greater Puget Sound area. http://www.gundies.com/ Their website says that they offer free delivery to Seattle and Portland.
Also, just FYI, and you may know this, the days of taking your toolbox and "browsing" the wrecking yard are long gone. F***ing lawyers ruined it. They can look up and check if they have a specific part, and if they do, they'll pull it for you, but I don't know any commercial yard that still lets you go out onto the lot.
The only exception to this that I've ever encountered is Lummi Auto Recyclers, out on the Lummi Reservation in Whatcom County. This place isn't so much a wrecking yard as it is a few acres of broken down cars in the grass and bushes. There, you still do take your tools and go pick. You then go to the trailer at the front of the property and haggle with the friendly folks who run the place. It's like Mexico, it's kind of expected that you'll haggle on the price. I went out there three years ago for a truck part, they said $30, I said $10, we settled on $20.
They don't have a website, just a phone number: (360) 758-2061 and the address is 2544 Cagey Road, Bellingham. Also, I don't know how familiar you are with Native American culture, but they operate on "Indian Time." They're open when they're open, they're shut when they're shut. Call before you go.
Also, if you can't find it locally, try Ebay Motors. I found an impossible to find rag joint for my 73 Ford in New Jersey on ebay motors.
Sorry I don't have any King County resources for you. Whatcom County is the only place I know of that has any of this stuff left. You would think there might be something in Pierce County, but I'm not as familiar with that neck of the woods. Perhaps somebody else here on Qland knows of a Seattle-area resource that I don't. Otherwise, you might plan a trip North.
Good luck.