did you try cleaning up the contacts? a pencil eraser works for that. Or bending them out a bit so they make better contact.
If all else fail an auto-electric shop could probably adapt something for you that uses a standard turn signal bulb. I’ve never had to do that on cars, but sometimes had to do it on home lighting fixtures that came with weird bulb connections.
The turn signal uses a standard bulb similar to an 1156A, the way the socket mounts to the headlight is unique.
Well, I certainly hope the replacements come through and you’re back up and running soon. I know what I would do if faced with this problem on a 13 year old car. I’d buy the closest common replacement socket, modify it to at least fit into the headlamp assy hole, splice it into the harness and then use a bead of that peel-able window sealant to secure it into the headlamp assembly. If, for some weird reason, I still had the car when those lamps failed, you could easily pull the socket back out and swap the bulbs. Then re-seal it back in the same way. viola! 
1 Like
Got help from: Nevada-_545 in his 7/23 post @ 4:50 PM showing a link to ebay.
Clicking on the ebay link shows photos of the socket insert.
A later post from Nevada_545 says it all: the socket is “unique” design - it uses a standard bulb but the way it installs into the headlight housing is unusual.
Many thanks to all those in the “car talk community” who have assisted in this “search.”
Unfortunately the one of contacts “burned” through because, I believe, it “wobbled” repeatedly in the housing. I tried closing the burned hole by soldering it but it didn’t work. When the “wobble” happened an " electric arc" was produced which, I believe, caused the “hole.”
Assuming the new ones I ordered with the help of car talk’s Nevada_545 I should be up & running soon! Again, thanks to all of the car talk fans who helped in this.