My first thought was it'll be a lot easier to maintain if they put some sandpaper-like grip tread on those wooden ladder/stair steps. It comes in self-adhesive rolls, you peel and stick. Huge safety improvement for very little cost.

Without modifying anything intrusive to the mechanism, a cheap way of monitoring to make sure it's still running OK would be to install a low cost PoE IP camera mounted in such a way that it's aimed at the gear mechanism, then feed its video into something like Frigate. As cheap as $75 for a camera, some cat5e cable and staples to take the cable to where you need it, and an old desktop PC (plug it into anything that gives it a DHCP lease and default route outbound, make it a VPN client). You could also possibly use the camera to monitor the blinking status LED without doing anything intrusive to the existing electronics.

One other random thought: The battery in that photo looks like exactly the same size commonly used in emergency exit stairwell wall mounted battery-backed lighting systems, it's a 12V 7Ah to 8Ah AGM lead acid, rectangular/flat size. It should be fairly easy to find a replacement if needed from a local distributor of commercial electrician supplies/parts. Those things should go on a fairly frequent replacement schedule since they're held at 100% state of charge near constantly, and that one is probably exposed to hot summer sunlight temperatures in June/July/August. As a general rule if you don't know how old it is or have any records of when it was last replaced, it's time to replace it.