Hi again Jimmy,
Your pictures in BritBike clarify a number of questions and assumptions here
Your pictures show a 25A blade fuse - 25A 'continuous', 50A 'blow' - and what looks very like 14-strand wires ... So, if the 'short' was drawing more than, say, ~10A and less than 25A, that's the wires done for without blowing the fuse ...
>>I opened the headlamp and again the brown/blue had melted as well as the white/brown wire.
The pictures show both the Brown/Blue and Brown/White attached to the Ammeter melted. That rules out the Ammeter as the problem, as current from battery -ve (assuming standard "positive earth" passes through the Ammeter; if the short was from the Ammeter to, say, the headlamp shell, the Brown/Blue would be melted but not the attached Brown/White.
When tracing for the cause of the short, look where the melted Brown/White wires go - as standard, they go to rectifier, Zener and ignition switch; whichever's melted leads towards the short ...
Just a thought but, if the melting doesn't go into the White/Brown - lighting switch - or plain White wires attached to the ignition switch, the cause of the short is the switch ...
Btw, 'fraid your pictures show the existing wiring is utter carp - apart from the 25A blade fuse and the red- and blue-insulated bodger's terminals, no thought has been give to insulation certainly within the headlamp shell - e.g. insulated wires and terminals attached to exposed ammeter terminals ... FFS!!! 'Fraid the problem you've experienced was only a matter of time ...