Check the rectifier: one diode may be bad: it will measure as "leaky' in the reverse direction, but still sorta working. I used to see this when guys would charge the [low or dead] battery with a 10 amp or larger charger, already turned on, and then clipped to the battery in the bike.
The PIV for most of the bridge rectifiers was only 25v until (officially) the K2, but the old rectifiers still showed up in the bikes after that if someone found one at Honda. The newer ones were/are 50 PIV rated, and the brand-new ones from 2005 or so are higher yet, said to be 75 volts or more.
So that will cause all the extra juice to heat up the fuse?
Yep, I've seen it several times. It was hard to diagnose the first 2 times, after that I just dubbed it the "symptom of too big of a battery charger in the garage" syndrome.
Back when I had my shop, it was out in farm country. Everyone had battery chargers with wheels built into them (100 amp/25 amp switch on the side), made by "Sauer" (or something like that) from the local discount superstore. One day I happened to see one plugged in at the store and went and got my voltmeter from my car: the open circuit voltage on the big cable clips was 90vDC(!) with the switch of the charger set to "HI" charge mode, and over 40vDC on "LO" mode. Then I figured out what was causing the failed rectifiers. It wasn't happening to just the Hondas, but the Suzys we sold, too, and always in Spring. The failed bikes belonged to kids who lived on farms, so it made sense: I told LOTS of [anyone who would listen] riders to use trickle chargers instead. That seemed to slow it down, at least in that town. Curiously, the 750 would fail a diode in the upper half of the rectifier, between the AC input from the alternator and (+) voltage, never on the (-) side. From that I surmised the battery chargers were electrically (transformer) isolated from the building power input (power cable), which all made perfect electrical sense. Still does.
If the hi-output charger is one of the uber-cheap modern ones it won't have a transformer, but a chopper circuit (like either triacs or SCRs in a triple-bridge configuration) that is driven by a waveform-chopping IC that slices off pieces of the AC waveform to make a lower charge rate: these can utterly destroy the old rectifiers in these bikes if the charger is plugged in (i.e., ON) and THEN attached to the battery. It only takes tenths of a second to adjust in the charger, but during those tenths-of-seconds the voltage is more than 400% of the rated PIV of these rectifiers. They can't take that for more than a few milliseconds without damaging their PN silicon junctions. It doesn't fully short them through: it just makes them 'leaky', generating lots of heat, because before they can fully melt into a short, the charger reacts and drops the voltage. But, that's long enough to hurt things.
