Following some advice from more seasoned builders of Jacob's Ladders I added the two 1MΩ resistors to one side, this makes the arcing much more reliable. Prior to this, quite often the arc would snap at the top and then fail to reignite.
The aluminium plate is a heatsink for the power transistor (its predecessor was fried during early testing). There's a tiny LiPo inside, battery life maybe four minutes.
The laser-cut box is 45mm x 45mm x 17mm. With the wires in place it's about 15cm tall.