The concept is pretty straightforward. The smaller the inverter, the better. The more mAh the batteries can deliver, the better.
I started with a MakerBot filament spool and removed the label.
The CyperPower CP175 inverter works great (from Best Buy), but is a little large. I had to cut a hole in the spool to accomodate it.
Whatever inverter you choose, get one with a separate cord like this. It is easier to cut these wires and attach them to your AA batteries than to fool with some "integral inverter/plug."
Print the "lamp bracket." This will fit in the upright tube, fit in the MakerBot spool, and hold the threaded brass piece from the GE bottle lamp kit.
Thread the insert in the large end of the bracket.
Add the adapter and ring.
Drill a 1/2 inch hole in the side of the spool. Cut the wires to the desired length and run them through the socket cap.
Attach the wires to the socket.
Add the socket shell (with the insulating cardboard) over the socket.
Snap the socket cap onto the socket and screw the lamp bracket to the socket.
With the lamp switched to the "on" position, slide the assembly through the spool (you may have to cut part of the switch off). In you are uncomfortable with the friction fit of the spool, add a screw through the spool into the lamp holder assembly.
Print a lamp base.
Slide the clear acrylic tubing (1 3/4 inch OD, 1 3/8 inch ID, one foot long--Amazon.com) into the base piece.