Battery charger only puts out 11.5 volts

OK try this...
Get a small 12v bulb like a car brake light bulb.
Temporarily wire it in SERIES between the battery and the charger.
If the bulb filament glows when the charger is plugged into the wall and does not glow when the charger is not plugged into the wall...then
that means the charger is probably working fine.
The glow indicates the charger is pushing current into the battery.
The brighter the glow, the more current is flowing.
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