Without exact details of the charger circuit, there is no way to know. You could try just connecting a 12V bulb in series with it as a current limiter, eg. a car headlamp bulb.
The other simple solution would be four cheap 12V car chargers, one across each six cells.
If the cells are sulphated due to lack of use rather than just old age and over-use, an electronic "desulfator" may help - they are supposed to electrolyse the sulphate back in to the electrolyte, which increases its SG and to some extent restores overall capacity.
I've had mixed success with them on smaller lead-acid batteries from UPS units that have become unusable; some can have a lot of capacity restored, others do not change at all.
There are numerous DIY designs for the gadgets around, eg.
Or you can buy various kits and ready-built devices on ebay & amazon etc.
Plug in your 12 volts adapter to DESULFATOR input. desulfating will continue but at a slower pace. When lead sulphate crystals build up on the lead plates, it is not an easy task to remove them and thereby recondition the battery.
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Regardless of any claims of battery voltage, again I'd suggest connecting one across six cells and move it to a different section of the battery every week or so.
Background info: