I'm using 26awg (power & ground wires) or 30 awg silicone-coated wire (for data lines) for all steps. This wire is super flexible, heat-resistant, easy to use, and very hard to break. It makes the wiring on this project much easier using than traditional wire.
Color-coding the wire is very helpful too, as the wiring can get a little crazy otherwise. I'm going with the color-coding as I found it on my Dotstar strips. Manufacturing sometimes changes these colors around, so notice if your wiring colors are different and adjust accordingly.
For me: Power (5v) is red, G is black, Clock is yellow and Data is green.
Use a utility knife to carefully remove the silicone sheathing and most of the covering and glue from the ends of your 1M Dotstar LED strip where the connector is soldered on. Get the ends as clean and tidy as you can.
On the "in" end of the strip (arrows pointing away from that end), clip off the red and black (5v & g) wires, leaving the two center wires. On the "out" end, do the opposite -- clip off the data & clock wires (yellow and green on my strip) leaving the power wires intact.
Go back to the "in" end and count out 36 pixels. Count them once more. Then, with tiny scissors or a utility knife, VERY CAREFULLY cut between the pixels as shown. Leave the two center pads on the "in" end, and the two outer pads on the "out" end of the segment. (hint: this is easier if you do it from the back of the strip)
Repeat with the rest of the pixels until you have 4 equal strips, with clock and data pixel pads on the "input" ends and power and ground pads on the "output" ends.
You may not need this fancy cut in the middle of the strip, if your strip has a solder joint there -- just unsolder and you've got four full pads on each strip you can use.
Cut 3 short (2-3 inch) pieces of yellow & green wire. (You only need 3 because one of your strips already has the wires soldered on, fancy that!) Solder the yellow wires to the clock pin and the green wire to the data pin on each of the 3 LED strips, copying the layout from the 4th strip.
Cut 3 short (2-3 inch) pieces of red & black wire. Solder the red wires to the + and the black wires to the - pads on the other ends of the LED strips, copying the layout from the pre-soldered one again.
This is a great time to hook up some aligator clips and a gemma or flora running the Dotstar strandtest code to be sure all your LEDs turn on and your connections are solid. Once you're happy, cover the ends of the LED strips in hot glue to reinforce these tiny solder points.
Lay the LED strips along the wooden dowels, making sure they're an equal distance from the *battery* end (the middle) -- remember, these two dowels are different lengths, so aligning them with the outer edges of the dowels will give you an off-center staff. Leave an inch or two of dowel at the outer edge, so your LEDs don't get blocked by converging wires later on.
Use a thin layer of glue (hot glue works great) to secure the LED strips to the dowels. Be sure not to pile it on -- you want a low profile here so the whole thing fits nicely into the tube.
Put a dab of glue on each end of the battery and glue the dowels and battery into a long line. (Note: this glue is merely to make wiring and layout easier, it doesn't need to hold structurally). Be sure to align the dowels the same direction, with the LED strips lining up perfectly on both ends.
Bend the wires on the on/off switch 90 degrees and secure the switch to one end of the longer dowel with a dab of glue.
Then, solder two long wires to the end of the switch leads. One wire will need to reach about the middle of your staff, and the other will need to stretch to reach the other end, so leave these pretty long.
Twist the two data wires and the two clock wires together at each end of the staff.
Find the end with the switch. Splice a long (3 foot) piece of color-coordinated wire to each twisted pair. This wire needs to reach the corresponding twisted pair at the other end. Run this wire down the opposite side of the dowel from the switch wires.
Pull the two red wires from the opposing LED strips to the same side as the switch wires and twist into pairs.
Pull the black wires to the other side, and twist them into pairs too. Splice another short wire onto each pair, long enough to meet near the middle as another twisted pair. (Mine are off-center so the joins don't compete with the battery for tube space) Leave these alone for now, we'll hook them up a little later.
At the Pro Trinket end, connect the green & yellow clock & data wires together, splicing one more short wire in to each side for the run to the Pro Trinket.
Whew! Our LED strips and switch are mostly wired up. Set this assembly aside. Maybe have some chocolate.