The right side light arm has a stop which was broken off. The result is that the light tends to just fall flat. It was pretty apparent what had happened once I opened the lid.

The left, working side:

The right, broken side:

The broken off stop was screwed into a tapped hole. It was a pain, but with a small screw extractor, came out. The threads were M4, so I had fewer options. I substituted a screw that I had lying around which worked, but the head hit into the plastic top cover when it was installed.

Some work with a dremel, and the head was removed and replaced with a slot for tightening.

This fixed it perfectly. I didn't bother trying to bend the metal tab back to straight as it didn't seem to have an visible difference.