Cut two pieces of white fun fur about 2.5 inches wide and slightly longer than your LED strips.  Cut two pieces of 1/4" trim to the same length, and 4 pieces of ribbon to about 2 1/2 feet -- just long enough to tie the bandoliers onto your costume.

Find the top end of the fur strips -- the end you want to start petting from.  Line them up with the furry sides facing inwards.

Sew along the left and right edges for about 1/2 inch: enough to hold the two strips together, leaving a hole in the middle large enough for the Gemma to fit through.

Stitch two ribbons securely to the free ends of both fur strips.  You can use a sewing machine or hand-stitch, but it helps to use heavy duty thread for strength.

Cut a small piece of scrap fabric the same width as your fur strips and wide enough to hold the Gemma and your battery.  Sew one of a small piece of velcro along the top edge as shown.  Sew the other side of the velcro to the back side of your fur, next to the center seam.

Line up the velcro, then hand-sew the other three sides of the fabric to the back of the fun fur.  Be sure your battery fits nicely inside, and be sure the velcro keeps it in place.  Slide your Gemma into the pocket through the hole you left in the fur's center seam, with the LEDs emerging on the furry side of the fabric.

Place your LED strip down on the furry side of the fur strip, face down.  Make sure the wires going to the Gemma are well hidden.  Place your 1/4" trim over the back of the strip.  Hand-sew the strip and trim in place, catching the silicone sleeve but not piercing the actual LED strip with your needle.