I've been on the road for a few days, just got to this now. Really dig the Drag Nut model piece!
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With today's clue, I'm going with "water bottle screw top" as my guess. Doubling as a radiator cap....water....cooling for the Top Fool.
We all run into those snags with our builds that set us back some. You have put an immense amount of work into this. Bring it on home!
Is 406 the 20" tire size you want? What are the dimensions of your rims again? If they aren't Schwinn specific rims, most tires that aren't labeled as such should fit a conventional ' 20" ' rim.
Try this site:
https://www.jbi.bike/site/
Go to Products, then Tires, then Clincher, then 20".
There will be dozens of options. J & B Imports is a national wholesaler with many distribution centers around the country. There will be an LBS near you that has an account with them, and will order from your nearest location. If you find a tire you like, go to the drop down tab in the item listing, click on it, and it will tell you if it is in stock at all the various distribution centers. You can check all the dimensions, tread, etc right there, and submit the part # to your LBS, and they will be able to tell you the price based on that.
J & B carries many of the name brand 20" tires, and some you haven't heard of likely.