The USB camera stuck inside the lid of the laser worked fine:

Until a month or two ago, when it began disconnecting randomly.
The camera cable has a standard USB A connector on one end and what looks like a 1.5 mm JST ZH connector on the other:

Of course, it’s not quite long enough, so it plugs into a good-quality 1 meter USB 3.0 extender to the PC sitting atop the laser cabinet.
Some low-effort tweaks were unavailing:
- Different USB ports
- Different USB extension cable to the ports
- Hub vs. direct
Eventually, some rummaging in the Box o’ USB Cables produced a cable from a different camera and, as you might expect, swapping the two identical cables solved the problem.
I have no idea what’s going on, but I’d lay significant money that when this cable gets flaky, swapping the original cable back in will solve the problem once again.