the tube looks clean if gas comes through & no need to remove the tubing [mine was plugged with oily sawdust & cleaned it with wire pushed through], try to run the engine spraying fuel-mix into the carb, I always do that before getting into the carb
I have the same Mustang & color, that copper tubing is the vent & goes up to the top of the fuel tank, can be seen next to the fuel cap opening, maybe the needle valve needs to be adjusted or the hole cleaned [built up dust due to long storage], also the idle RPM maybe too low, when starting give it a bit throttle