I'm trying to charge a 6-year-old OEM lead-acid battery in a 2008 Volkswagen Jetta with an external charger, whilst it's still connected within the vehicle. (The battery was working fine, until it got discharged to perhaps 25% due to a prolonged episode of charging the mobile phone through the car without the engine running, and wasn't recharged fully since then; I've now added distilled water, and am trying to recharge it after a delay of only a couple of weeks since the last proper charge.)
When tested under slight load (key in the ON position without the engine running, and with the lights off), it would appear that the voltage of the circuit being charged is only about 12.6V or so; when testing under no load, it's maybe around 13.5V (with the charger being in maintenance mode).
Is there any point in trying to recharge a sulphated battery with a charger that appears to only be capable of producing merely 13V in its maintenance mode, for a 12V battery? Would I have a much better luck with 14V for trying to de-sulphate my battery?