Welcome to LVC! There are many amazing knowledgeable people on this site. You'll find a lot of info on here.
Your Mark VIII looks really good. Its good that it came from California, no rust. I believe the blend door could also be causing your problem. The fuel issue do you see or smell fuel on top of the engine at all? The fuel filter on the Mark VIII's is on the passenger inner wheel well liner, behind it of course. Might be a fuse of some sort. Look for any stored codes if you can. For the neon taillight, Glitch use to sell a ballast for this problem. I don't know if they do but I'll provide info as to places that have Mark VIII restoration parts.
1. Super Coupe Performance
2. Temple Performance
There are also Facebook pages on the Mark VIII:
Lincoln Mark VIII Marketplace
Here is a Facebook page dedicated to a group who own and have regular get together's in your area:
Lincoln Mark VIII Addicts
https://www.mk8addicts.com/
I also want to point out LCOC Lincoln and Continental Owners Club. It costs $48.00 a yr. You get a monthly magazine, meetings and greets all over the country. You get a good price on advertising in their magazine if your selling something, or promoting a business. Best of all you get Ford X- Plan discount on any new Ford or Lincoln whether you buy or lease. The more popular the model the more you save.
Can't wait to see more of the car! Have fun.