As I was rebuilding this, the first step was disassembly. Easy, I unscrewed the cap, and fished out all the wiring. Untangling it all took some time, but wasn't particularly difficult.

I spread the wiring out on the table with the ends hanging off, and a weight holding it in place.

The light strings I used were originally battery powered, and had 10 LEDs in parallel, with a 6.8ohm 1/4W series resistor built into the battery pack. To match the voltage drop and LED current, I used 6 strings, connecting them in series with two of the 6.8ohm resistors to power off of a 14.5VDC adaptor I had handy at the time. There were 3 of these circuits wired in parallel off to total 180 LEDs.

You can see series circuits spread out in the picture above, with joints covered in black electrical tape. Two of those joints have 6.8ohm resistors in them.