I had a FM with a non-functioning light meter. I sent it to Garry's Camera Repair for a CLA and repair if it could all be done for the cost of the CLA. Garry wasn't sure he could repair the meter, said it depended on what was wrong. Turned out it was a badly corroded (vitually destroyed) battery compartment. He performed the complete CLA and rebuilt the battery compartment for $53. It is slightly different than original, but works fine. If it were mine, I would send it in for an estimate. Garry was very responsive to my inquiries.
We are so lucky to still have these great guys around who do great work for such great prices, like Hendrickson with my Pentaxes.
I do use a digital device in my photographic pursuits when necessary.
When someone rags on me for using film, I use a middle digit, upraised.
The problem with my FM was that the corrosion was in the compartment itself, not necessarily visible on the contacts. The wires had corroded and needed to be replaced. My point, the problem may be deeper than is readily visible and cleanable, but still not insurmountable if the camera is disassembled by a knowledgeable person.
That said, I have heard of folks using a pencil eraser with good success, also fine grit sandpaper or emery cloth could probably help without causing serious harm - use care not to bend or deeply abraid. I've also seen folks refer to a commercial contact cleaning kit that consists of two fluids you apply, one a cleaner, the other a protectant. I don't recall what the name of the product was, it is suggested often for lens/camera contacts that get finicky.
A small bit of vinegar will take out corrosion, I used this on an old vivitar flash and it jumped back to life! I would be careful and maybe just soak a q-tip in the vinegar and try not to let some get into the camera. Short of this, I would send it out for a CLA as suggested as it probably needs a good cleaning too.
I have unfortunately bad news. I went the camera to a repairman and he told me that the camera isn΄t fixable because the problem isn΄t in the battery contacts or the wires but is more serious and he can't fix it because he has't any spares. So I will return the camera to the shop I bought it and pick another. The available options are a Pentax ME, a Fujica AX-1, a Olympus OM-10, a Nikon F90 and a Nikon F90x. The Fujica has a X-Fujinon zoom and for the Nikons I can keep the Nikkor from the FE-2. So my question is which camera should I choose;