A colleague of mine started talking about having resurrected an old Olympus OM-10 which his father had abandoned in the 1990s. Sparked by that, I decided to check what state my OM1n and OM2 were in. I'd last used them regularly in about 1994, and I was pretty certain that the batteries hadn't been changed since then.
The OM2 was fine. The battery compartment opened up, and a pair of spare silver oxide batteries that I had in the case turned out to be perfectly sound. The camera fired straight up. I'd had it serviced shortly before it stopped being used, so the batteries in the camera and the spares probably dated back about 20 years. That the fresh ones still worked was pretty miraculous (and I've ordered a new pair to be sure), but the ones in the camera hadn't come to too much harm.
Luckily, the seepage was into the interface between the two batteries, rather than into the camera itself. With new batteries the metering is at least internally consistent and appears to give sensible readings, and dry-firing the camera shows that slow shutter speeds are slower than fast shutter speeds. The auto seems to open for longer the less light there is. Overall, it looks like the camera's sound (given it was made in 1978 this is rather nice).
The OM1n, however, is a bit more serious. The battery that uses is a 1.35V mercury cell which is now unobtainable, but more seriously the battery hatch is jammed solid.
Gingerly I removed the base of the camera
By the time I took this photograph I had cleaned the battery compartment, but the original state of the battery was pretty grim.
The rectangle in the first picture is the impression left by the contact strip. Given it's a mercury battery and mercuric oxides are nasty stuff I washed my hands very carefully after handling it. Unfortunately, the gunk from the battery has gone into the threads of the battery hatch, which is still jammed. People on t'internet recommend all sorts of caustic options, but initially I'm just soaking it in some penetrating oil to see if it will free off. In the picture below the oil has already cleaned off the worst on the inner face of the hatch, but the threads are still resolutely jammed.
Update: an hour of soaking and it could be opened, with the threads not looking in too bad a state.
Update update: with the help of the Small Battery Company, I now have a Wein MRB625, which is a weird Zinc-Air replacement for the banned mercury 625 1.35V battery. It's not a long-term solution as apparently it only lasts a few months; Zinc Air batteries use oxygen from the air to provide a lot of power for hearing aids, which is fine, so long as you want the power to be continuously developed. However, SBC also stock a converter to allow a modern 1.55V 386 battery to be stepped down to 1.35V, while fitting into a 625 formfactor. Assuming the first few films through the OM1 check out OK, I'll get one of those.