Thanks for the nudge. I searched the manual, nothing. I emailed Cateye tech support: nope, can't turn it off, no way to extend battery life. GPS speed tracking does automatically turn off when it syncs to a speed sensor. However that doesn't turn the GPS itself off, just its speed calculation since that is hopefully supplied more consistently by the wheel sensor.

Interestingly and kind of along that line, I have the Edge 800 set to automatically calculate wheel circumference from its GPS inputs. Then it's easy to read that off the Edge and put that number into other computers, like the Cateye, which don't have that bit of smarts, without having to measure it.