The 64 1/2 is a unique pony. My little sister got an original paint convertible when she was 16 back in 1977 and she still has it. If you're restoring it a "lot" of little things will be different and it's important to not change them. You will increase the value of the car keeping it as original as you can. You can hot rod it but just be sure to always keep any original parts so they can be put back on. All the original casting numbers, manufacturing date codes on parts are an important part of the car's history.
I can't help with the top. MY sister had a guy make a top for hers back in 1977 and it turned out real nice but how "authentic" it is I don't know. BY now there must be some good reproductions You can probably order a better fitting "original" top than someone will make for you. But before ordering one you need to check, is a '64 1/2 top the same as 1965, the stitching... Every time you do something you will need to check that it is correct for a '64 1/2, it's a weird Mustang. It super cool it an early production but some things are a pain like having a generator instead of an alternator. You really need to be on one of the Mustang Forums. Hopefully the door tag is still there, and you look up the build date and all the originals details.
The speedometer cable probably needs to be lubed. Undo it from the back of the speedo, pull the cable out from its housing and wipe it clean. Lube it with white grease. Some people say to use graphite, but we always used white lithium grease and it always fixed the problem. Easy job to do. At least I think it comes out the top it's been years since I did one. I worked as a mechanic for the phone company for 30-years and sometimes work vehicle repairs and my Ford repairs get a little mixed up. Some cables pull out from the top and some the bottom.
If you disconnect the wire from the sending unit, this is the variable ground for the gauge. With the wire off the gauge should read empty because it has no ground If you ground the wire directly it bypasses the sending units' resistor, and the gauge should go to full. That should tell you that the gauge and the wiring are good. If that checks out you will need to remove the sending unit and see if it does swing all the way up and down, maybe its rusty getting stuck at halfway. Hook the wire back to it and give it a ground wire from its mounting flange to ground and operate the float up and down. That will tell you is the variable resistor is working correctly. Another easy job except for draining the tank. Run the tank down as empty as possible before removing and keep drop lights, electrical cords... away while working under the car. Jack up the back of the car, use "good" jack stands along with the jack, chock the front tires since jacking the car up will eliminate it being in gear and eliminate the parking brake.
One thing you can try is to pull the fuel filler neck and hose from inside the trunk. Maybe you will be able to get an inspection mirror in there and see if that float arm is getting stuck halfway down and maybe free it up through the hole. That rubber hose might be cracked and need replacing anyway. The hoses would crack and fill the inside of the car with fuel fumes. The tops of the tanks would get rust pinholes from the trunk mat padding getting wet. So, check that out too. It its rusted through you will be replacing the tank. Rust and gas varnish inside the tank are one of the main causes of breakdowns on old cars. if you can see in the tank inspect it for rust. I've had 15 early Mustangs and have had to replace the tanks on several of them and those supposedly rust-free Southern CA cars. Some of them were nice original cars but almost all of those floor mats and trunk mats would get wet and stay that way and rust out whatever they were laying on top of no matter how well-maintained the cars were, garaged or not. Just about all the windshield gaskets split and leaked on them when they got to be around 15 years old. The windshield gaskets and floor mat padding is what rusted CA Mustang floors and gas tanks.
How to check a sending unit
https://www.youtube.com/watch?v=FTFpbTVv3OM
