Choose one Neon strip to use as the costume's head. Solder about 15-18" of additional wire to the red and black wires -- enough to reach from throat to belly button.

Cut another 15-18" of red and black wire -- enough to go from belly button to the pocket where you plan to stash the battery pack plus a few inches of slack.

Strip about 1/4" of shielding from the end of each wire and twist the two red wires together and the two black wires together. Set this piece aside.

Trim the wires from the 4 remaining neon strips to about 1-2 inches long. Twist the red and black wires from 2 of the strips together, then repeat with the other 2 strips. You should end up with three bundled sets of 2 twisted wires in red and black.

Twist the red wires from the head together with one of the paired strips for the body. Slide your heat shrink over the four wire twists.

Twist the remaining body sections into the mix and saturate the resulting 6-wire joints with solder. Be generous with the solder here - you want to be sure the connection is strong and includes all 6 wires. 

Attach your screw terminal to the power wires with a screwdriver, making sure the connection is tight and the wires won't pull out easily.

Plug in your battery pack and flip the switch to "on". Test to be sure all the neon strands light up. When everything is working, use a heat gun to shrink your heat shrink over the wire connections.

Cut the wires going to the head strip near the wire junction. Slip on a little heat shrink on all 4 cut wire ends.

Solder a JST connector to the cut wires, making sure to line up red with red and black with black. 

Now you can connect and disconnect the costume's head as desired.