Should you have constant power to the fuse box on a 77 Chevy truck?

No, you should not have constant power to the fuse box in a 1977 Chevy truck (or any vehicle for that matter). The fuse box needs power only when the ignition is on (or in some cases, accessory power as well). Constant power would drain your battery and could potentially cause other electrical problems. The fuse box itself usually has both switched (ignition-controlled) and unswitched (constant) circuits, but the entire box shouldn't be constantly energized.