I would connect a known good meter to the charger connection at the battery - charger unplugged from the outlet - and note battery voltage. Then, plug the charger in the outlet and observe the charger output at the battery.
Good battery should be in the 12ish range. Good charger plugged in and connected to battery should be around 13 - 14 volt range or so.
I install a small digital readout on top of all my battery maintainers tapped into the leads. When I connect it all to my battery, I see battery condition. When I plug it in at the wall outlet, I see charger output. On mowers, motorcycles and such, I unplug it from the wall outlet, crank up the engine, and see the alt/gen/stator performance (Also in the 13 - 14 volt range).
That's how I discovered a bad 9 year old battery maintainer just last week. Just out of the blue, it started jumping around between 13 - 17 volts and I happened to notice it as I was walking thru the garage.
Unfortunately, chargers don't last forever. Good to find the bad ones early before it gets expensive!