This sounds very strange, I don't think I've ever heard of a fuse slowly melting. The idea is that they blow before damage is done.
So it probably isn't a dead short. It could be something creating a large load or high resistance.. The fuel pump we have covered and this is still to be checked. The only other thing I can think of that would create a high load would be a super headlamp bulb of illegal proportions. You can get very high wattage bulbs for off road use only, might be worth checking that, unless of course the headlights are not even on when this happens?
I'd be looking for softened cable insulation. It usually shrinks back from ends and tried to wrinkle up, sometimes it will melt and reveal conductor and distort connector blocks too. If you can find evidence of that it could narrow things down. Have you had a feel round for warm cables when the fuse goes?
I think you need to get a multimeter on the battery to check the voltage too. As mentioned before, it shouldn't exceed 15 Volts really. You should see up to 13.5 volts when switched off. This will go up to no more than 15 volts as the revs rise. Also expect a large drop when the starter is engaged, it should recover from that immediately.
If you are getting 17 or more volts into the harness then it will certainly damage things, starting with the battery.
I think the "missing" and fuse melting are separate issues. Concentrate on what is blowing the fuse and then address the misfire if it still present.
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