Sometimes, the wire leading to the center contact becomes corroded. That may be what's happening to yours. As the corrosion (you can't see it, it's inside the camera).
It is possible to check and possibly repair the issue yourself, depending on how mechanically apt you are. All you need is a 2.0mm JIS screwdriver to find out. (you might get away with a small 'phillips' jewelers screwdriver, but you run the risk of damaging screws)
Start by removing the battery, and lay it and the battery holder/cover aside.
Remove the three screws that hold the bottom plate on the camera. Important note: Although all 3 are the same thread size & pitch, the middle one has a slightly smaller head. So you'll need to keep track of that one. Once the 3 screws are safely stowed away, separate the bottom cover of the camera by pulling it straight away from the body.
The place where the button battery sits is a small, molded plastic piece held on by another 3 screws. Remove those screws. There might be a small wire in the way of one, so you'll need be carefully move it out of the way. Then, the plastic battery part should simply lift away from the camera. But don't pull too hard.... there's a wire attached to the other side.
Or..... is there? If the connection got corroded, the wire has become disconnected from the battery terminal attached to the plastic piece. If you have access to a small soldering rig, you can simply resolder the connection and reassemble everything.
Presto! A working K1000 meter!
I've rejuvenated 5 or 6 K1000s 'dead meters' this way over the years.