Hey David,
I don't know '62's but I am very familiar with '63 to '66. The fuel sending unit wire lands at the fuse box. There is a single blade connector socket on the fuse block that's labeled "gas gauge ext." it's located right above the plug for the red cigarette lighter wire. It is a switched power source that comes through the fuel guage, from the switched side of the ignition, and goes to ground at the sending unit in the tank. The 'sending unit' is basically a reostat or a variable resistor that changes resistance depending on the position of the float in the tank. Grounding is crucial here at the sending unit!!! If there is no ground, or if there is an open circuit somewhere along the line, the guage will peg at full as soon as you turn on the key, if there is no power to the guage, or if the guage is faulty, it will not register at all.
The wire is "brown" in a '63 and it's "tan" in '64-'66. If you're looking at the fuse block dead on, it's the second single blade connection from the bottom left. I hope this helps!
---The Hilander