Broken fuel line quick-connect

Well, you could do what I did and buy the Doorman 800-300 kit. Then you KNOW you've got the right size!

Ok, the 800-063 is the wrong style connector. You need something like the Dorman 800-058 or 800-082 (assuming it's 3/8" steel and 3/8" nylon). If you don't have the insertion tool, -058 with a short length of nylon line to a brass insert and crimp clamps is probably a better choice than the -082 type, which are very difficult to insert by hand. Even so, warm the nylon line in a cup of hot water for a minute before inserting.

If the steel is rusted out, you will also need a repair section with the bead -- something like the 800-155 can be cut to length, or the 800-230 which includes a 90° bend.

Ideally, the steel line repair section should be jointed mechanically. A compression or flare coupling is pretty common, but those do rely on having a smooth surface to work with. I have repaired fuel sender lines by cutting back to the least pitted straight section and silver-soldering a piece of 5/16" inside the 3/8" tube (may have to gently ream the inside of the 3/8" tube with a drill bit first). The very short bit of restriction doesn't seem to bother performance. You must be absolutely damn sure there's no gasoline in the line when you solder it -- which means removing the tank and disassembling the sender first, so this is not a quick fix.

Of course, the fastest way is to use 3/8" rubber fuel hose, as long as the steel is not too rusty. Clean it up as best as possible. If you can, use a flaring tool to put the start of a flare on the end, for extra security. But most important: use fuel line hose clamps, NOT regular gear clamps. Gear clamps tend to pinch the hose unevenly and are more inclined to leak. Fuel line hose clamps encircle the hose evenly.

Forgot to mention: those -058 type repair sections come with ear clamps that need to be crimped on, similar to a PEX connection. If you don't have the right tool, you can gently squeeze the ears with side cutters -- obviously, taking care not to apply enough force to cut into the metal!