Fit the regulator somewhere convenient (above or below the coil is a good option)

Fit the new 12V battery. The widely-available 4Ah YTX5L-BS fits in the existing tray just fine. Use a bit of foam to isolate the battery from the engine vibration and a rubber strap to hold it in place.

Connect a 10A inline fuse to the battery positive lead and connect the other side to the brown wire that previously went to the 6V battery negative terminal (for negative earth)

To use a single-phase regulator, you need to join the orange and light green alternator wires and connect them to one of the yellow regulator wires. The white alternator wire goes to the other yellow regulator wire. To use a 3-phase regulator, connect the yellow wires to the three alternator wires. It doesn't matter which one goes to which.

Connect the black wire from the regulator to earth (for negative earth)

Connect the red wire from the regulator to the brown wire that previously went to the rectifier (for negative earth)

Connect the battery negative terminal to earth (for negative earth)