How do I make a camera take a picture 50 years from now without any power?

Your instinct about the battery is right. Even the best lithium primaries self-discharge slowly and the cells can degrade or leak long before fifty years, so anything that sits powered up is a non-starter. The trick is to keep the circuit completley dead and only generate power at the moment of opening, which points you at a hand-crank or pull-cord generator, the kind used in emergency flashlights. Wire that to a cheap camera module and it only draws current while someone is actively winding it. The opener becomes the battery. The catch is making the crank obvious and self-explanatory fifty years out. Whoever finds the box has no instructions, so engrave or print something right on the lid: 'wind this handle, camera runs for one minute.' A spring-driven plunger that fires when the lid comes off works too, but springs take a set over decades and may not have the force left to spin a generator, so I'd trust a crank the human powers themselves over anything preloaded.

Corrosion is honestly the bigger enemy than power. Conformal-coat the board or pot the whole camera in wax, use a gasketed box with a real seal, and toss in a few desiccant packs. Drywall cavity air cycles with humidity and anything bare will be green crust by year ten.

And keep the low-tech backup in there anyway. A note, some printed photos, maybe a roll of undeveloped film, all in a sealed bag. Film stock from today can still be developed in decades if someone bothers, and it costs you nothing extra. One more thought: test the whole rig in a closet for a year before sealing the wall. If the coating or seal fails, you want to know now, not when a stranger cracks it open in 2075.

Did a version of this for my old shop's 50th anniversary, buried a little box in the foundation pier with a pull-cord generator and a cheap camera module. The crank idea is solid, but here's what bit me: I do restoration work for a living and even the top-shelf silicone sealants are only rated around 20 years. So don't lean on the gasket alone. I put the whole rig inside a glass mason jar with a rubber ring, waxed the lid threads, then bagged that in foil. Overkill maybe, but glass does not care what year it is. Also make sure the crank handle is metal, not plastic, becasue fifty years of waiting turns cheap plastic brittle enough to snap on the first twist.

We did something like this for our church's centennial back in '76, and the thing that got forgotten was the picture itself. Whoever opens that box needs the camera pointing at thier face, so think about the lens angle and put a big painted mark on the box showing where to stand. My old wind-up 8mm camera had a spring motor that still ran fine after decades in a closet, so clockwork is tougher than people think, though the guy above is right that you shouldn't count on a preloaded spring doing real work after fifty years. One other thing from that centennial box: half the stuff in there was unreadable because formats died. Paper and a pencil beat every gadget we put in. Keep your camera project, but make the paper the star and the photo the bonus.

One thing I'd think about since it's a bathroom: that cavity's got plumbing nearby, so temps and moisture swing harder than you'd guess. Whatever you seal in there, keep it off the pipe side of the stud bay and wrap it good. I found a time capsule in a wall during a remodel a few years back and the paper notes were perfect, but anything electronic in the box was toast, and this was only after like 25 years. Also, will whoever finds it even realize they're supposed to pose? Might be worth a mirror inside the lid or something, so they can see what the camera sees while they wind it.

New here so forgive me if this is dumb, but why does it need to trigger on its own at all? If the crank idea works, couldn't you just put a plain old push button on the box too? Anyone curious enough to crack open a wall is gonna poke around and press a button that says 'press me'. I only ask because I stuck a cheap dashcam in my kid's time capsule at school and the motion trigger was the flakiest part even after a few weeks. A dumb button seems way harder to mess up than a sensor sitting around for decades.

Update: went with the generator approach, built a tiny hand-crank rig that only powers the camera when the box is opened, so nothing sits dead in there draining. Took the aiming tip too, painted a big arrow where the opener shold stand. Kept the whole thing on the far side of the bay away from the pipes, wrapped in heavy plastic. Wall goes back up Saturday.