I own a cheap pair of digital calipers and sure enough the power button stopped working a while ago. So to conserve power I would remove the battery when not in use, which inevitably led to me loosing the battery cover. I don't know how I've put up with just taping it down for so long. But I have a fix!
This design creates a mechanical toggle on/off switch on the calipers as well as new battery cover. No electronics necessary! Just print it off, pop it in and yer done.
It works by blocking the battery from touching the contact. The switch rocks back and forth on a corner, by pushing the rocker with your finger, a thin piece of plastic slides between the battery and contact tab.
Now the cover isn't perfect (due to calipers inability to measure themselves) as you can see by the stickers which I used to adjust the battery position. But as I have it working now I can't be bothered to further refine it.
The feel of the switch is quite satisfying. I actually find it nicer to zero the calipers with a quick flick back and forth than pressing the real button.