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I assume the static 13.04 batt voltage was taken right after you had ridden the bike not in much traffic idling which is batt voltage was a robust 13.04v's.

Those #'s are right in line with what i stated your battery voltage should be reading @ the battery so your good to go.

So if the stock original voltage gauge doesnt read the same or close to it in same cond it's likely going bad requiring replacement or ignore it.

Scott