I got a Stanley FATMAX RE-CHAGEiT 8AMP Automatic Battery Charger & Maintainer from Walmart for 29,97 USD, which appears to have three states of charging the battery -- detecting the voltage, rapid charging at supposedly 8A with the yellow LED, and then maintaining the charge at supposedly 2A with the green LED.
I've tested the voltage with the in-car 12V socket tester in my 2008 Jetta, which did read between around 13.7 and 14.2V when the car was running, but it seems to be only testing around 12.5V when the charger is attempting to charge the battery now (it started with mid 13V when I just got the charger, but after several days of use, never seems to get above 12.7V anymore, even if I turn it off, discharge the battery for a while, then turn it back on). This appears to be the case both when the rapid charge is supposed to be taking place, as well as when the maintenance charge.
Is this normal? Would a sulphated old battery (which only appears to work fine when the overnight weather doesn't get too close to freezing) accept any charge to improve its condition when the charger must only be supplying something like 13,0V at most? Should I get a different charger, one that would supply closer to the gassing voltage of maybe 14,5V?