Find a good place to mount the push button that will control the backlight. I chose to put mine on the left side of the calculator, as you can see in the pictures. This was a very tight fit though. Some other suggestions would be on the top or under the battery cover (if you want to be discrete).

If you want to get really fancy, you could find a way to trigger the button when the calculator is turned on and off. I've also heard of people using photodetectors to automatically turn the backlight on when its dark.

Carefully bend the EL panel leads so they fold around the back of the PCB. The panel can bend pretty far, just don't crease it.

Now install the board back in the front half of the case and screw it down. The EL panel leads will stick up through gap between the panel and the case. Plug in the inverter and make sure the panel is working.

Drill the hole for your button with a 9/64" drill bit. It may help to put the two halves of the case back together without the guts inside.

Use hot glue to mount the inverter and push button in the back half of the case. Fortunately theres lots of space inside the TI. Use lots of glue so the button stays in place when you push it.

Solder the - wire from the inverter to the - lead on the battery case. The inverter needs 3V, not 6V, so solder the + wire to the connector going between the second and third AA.

Finally you can put the two halves back together. Plug in the EL panel and arrange all the wires so they don't get pinched. Snap the two halves of the case together.

Before you screw everything together, put the batteries in and make sure it all works.

Now its time to take apart the inverter. Clip off the spring and solder some wires onto the battery contacts. The inverter will be powered by two of the calculator's AAs.

The inverter has two buttons, but they both do the same thing. Desolder the button on the side and solder on some wires going to your own push button.

Celebrate.