There's a lot of good advice within this thread, here's my experience with my old Hexhead with similar milage, although the diagnosis is slightly different it's always worth checking.
Mine started stalling/cutting out for no reason while out riding eventually failing to start.
Fairly common fault with Hexheads are the cables from the ignition switch become brittle the plastic insulation coating cracks and moisture gets in corroding the copper wires until they break.
Sometimes just turning the handle bars can give enough to make a contact and this is a good test to diagnose the issue.
The fix (if it is this) is to chase the three cables from (below) the ignition barrel into the cable loom under the headstock until you find a damaged wire.
Might be worth investigating.
Mine started stalling/cutting out for no reason while out riding eventually failing to start.
Fairly common fault with Hexheads are the cables from the ignition switch become brittle the plastic insulation coating cracks and moisture gets in corroding the copper wires until they break.
Sometimes just turning the handle bars can give enough to make a contact and this is a good test to diagnose the issue.
The fix (if it is this) is to chase the three cables from (below) the ignition barrel into the cable loom under the headstock until you find a damaged wire.
Might be worth investigating.