I’m troubleshooting now, with help from Jim at Flux.
The Beambox’s door sensor is indeed a reed switch where I thought it should be, and while I could have overridden it with a magnet, I needed a way to tell whether the state-toggling was registered by the software. It turns out that the first indicator in the Maintain interface tells us this.
Having now stared at that indicator for a while, I think it’s a top-down view of the Beambox. It is too abstract for me to be sure. But it does respond when I hold a strong magnet near the reed switch. In fact, it responds when I put the disc magnets in a suitable spot. And it responds even when I pick a spot by the magnet that’s meant to activate the reed switch.
So it looks like I now have a good use for those little disc magnets, or perhaps I’ll go find a thin, strong magnet that can be secured more firmly. What might be wrong? It is hard to be sure without opening the Beambox up, but I am guessing that the reed switch might have moved out of place during shipping—possibly also what happened to the workspace LED sleeve.
Doing this activates the door sensor. 
This activates it, too—in a more useful way.
About the cooling pump: Jim advised it has a blue LED that turns on when it runs. The light is visible through the reservoir, like this:
As you see, the pump’s light is activating, and I’m hearing the pump run. But do you see that bubble in the feed tube? That makes a sudden small jump when the pump starts, but it doesn’t get any further. I tried sucking the air out in case a bubble was preventing the flow, and this is all the air that was left. (I released the laser tube, and tilted it so the air could get out, while I backfilled at one end and sucked at the other.)
While the water isn’t flowing, the jacket is at least full now, and the door sensor is activated, so I thought I’d try a few laser pulses just to confirm that the laser is lasing. And it is! So there is some reassuring good news about my new Beambox.
With some luck, there will be something simple and easy that I need to do to get the pump running and then we can get onto some actual cutting. I’ve already drawn up a vector file to measure kerf width, but I will leave writing about that until the machine is ready to get working.
beamboxing 