Survey says: a six-degrees-of-freedom magnetic sensor coil for tracking the position of the controller.

Cracking open the controller, we find the (much bigger) emitting half of the tracker, and an 8.4 Wh battery to boot.

The copper shielding sprayed into the coil housings likely protects from RF interference, while letting the magnetic field through.

Interference could explain the tracker's odd placement, and this may be a temporary solution. It's "old" tech, and will probably be worse for left-handed use.