The orange indicator I added makes the key lock switch position on the OMTech 60 W laser perfectly obvious:

It is in series with the lower switch on the side panel:

Although I would have labeled those switches differently, the “Control Switch” handles the 120 VAC line voltage to the HV power supply. As you’d expect, when its light is ON, the power supply is also ON and the laser is ready to fire.
Those two pictures show the situation after I turned the laser power on a few days ago: key lock switch OFF, HV laser power supply stubbornly ON.
Whoops.
The “Control Switch” still does what it should, so I can shut the HV supply off when it’s not needed, but the key lock switch has definitely failed ON.
As far as I can tell, the moving contact bar jammed at the bottom of its travel against the terminals. Pulling the switch out of the laser jostled it enough to release the bar and it’s now at the top of its travel:

If it failed once, it’ll fail again.
OMTech’s Customer Support agrees it shouldn’t behave like that; a replacement should arrive in a few days.