This is a guide for all modern gentlemen who would like to show off their electronic prowess.
This illuminated pocket square is just the accoutrement to illustrate that you're more than a suit.
Despite your straight razor shave and that Steuben rocks glass you hold: You're a maker too.

Check out Draper 2.0 in action.

Step 1: Materials

For this project, you will need:

Pro Trinket 5v
Pro Trinket battery backpack
Lithium Ion Polymer Battery (be greedy!)
High Density NeoPixel Strip
Capacitor *optional*
Silicone Wire (three colors is ideal)
Perma-Proto Board
Power Switch
Picture hanging tape (diffusion material)
Double sided tape
Electrical tape
White Pocket Square

This is probably the first wearable electronics project that has plenty of space or a large battery, so feel free to be a little greedy. I found that 1200 mAh lasted for approximately three days of gluttonous use.

Step 2: Soldering the Board

Battery backpack

Using the extra long headers included with the backpack, solder the long portion through the bottom of the BAT, G, and 5V pins.
Solder the backpack on top of the Pro Trinket as depicted above.

Pro Trinket

Using the included headers position the Pro Trinket so that the USB port is at the bottom of the Perma-Proto board.
Solder the headers to the Pro Trinket, for all analog and digital pins along the sides.
***The BAT, G, and 5V pins will already have headers coming from the bottom due to step one.
Solder the headers from the bottom of the Pro Trinket onto the Perma-Proto board.
Clip the end of the headers off.
***Nail clippers are actually awesome for this.

Power Switch

Use an exacto-knife to cut the pads between the switch pins.
Carefully bend the pins coming out of the bottom of the switch 90 degrees so that the switch mounts flush against the Pro Trinket battery backpack.
Solder the switch in place

Capacitor and wires

Solder the capacitor into the power bus to the left of the board.
Be sure to pay attention to which lead is positive and negative on the capacitor.
This is optional, but also a good safety step.
Solder a wire between the BAT row and the positive line of the power bus
Solder a wire between the G row and the negative line of the power bus
Solder a data wire to the row you intend to use as your digital pin.
This is shown as the green wire.
I used pin 6, but it's hard to see because of the battery backpack.
Solder power and ground wires to the power bus near (but NOT AT) the top of the power bus.
The strip will be attached to the opposite side and I had some issues where contact with the strip caused a short.

Step 3: Soldering the NeoPixel Strip

This step is arguably the trickiest of business.

The contacts you have to solder onto are tiny
The data pin is uncomfortably close to the first LED

I'd like to share with you the best way I've found to reliably tackle this challenging step.
Tin the strip and the wires separately, then bond them.

You are going to need 12 LEDs, so carefully cut the 144/m strip.
Feel free to leave the ending pads on the remaining strand instead of splitting the tiny surface in half.
Apply some solder flux... errrr... apply alot of solder flux to the tiny pads.
Apply solder to the end of your soldering iron and tin the pads.

Be very careful to spend as little time in contact with the strip as possible.
It is relatively easy to ruin the surface mounted LEDs or melt them :X

Step 4: Tape Time!

Now it's time to attach the NeoPixel strip to the top of the board.

On the back of the board, apply some double sided tape.
Center the NeoPixels and firmly stick them to the double sided tape.
Use some electrical tape to further secure the strip from the Pro Trinket side.

Diffusion Techniques

Even though the cloth of the pocket square will apply some diffusion, it wasn't enough to get a uniform 'glow' across the entire square.

Try using some foam tape thats usually used to mount photo frames on the wall.
I used the velcro-ish type to get a pretty even glow.

Step 5: Folding

Here is a great overview on pocket squares.
There is a ton of variation in folds, but the most traditional is the square fold.
In a square fold, it's common to place an index card to help the square hold its shape.

In our build, the index card is replaced by a battery and LED board.

Reference the photos above for a quick and simple fold that fits snugly into your coat pocket.

Step 6: Future Enhancements

Sensors

There's still plenty of room on that Perma-Proto board to include some type of sensor.

A color sensor could be used to match your date.
An accelerometer could add a dimension of fun to dancing.
A bluetooth 4.0 board could provide a means for you to change your style on the fly.

Gentleman's Tip: Your pocket square should never match the pattern of your tie. Always aim to match the color of your shirt, or your date instead.