With a switch mode power supply and 13.2 to 13.4 volts a 12 volt battery could be left on for an extended time the batteries in fire alarms, intruder alarms, stair lifts and like can sit on a charger for years, but as the voltage increases so the time on charge needs to reduce, so 13.8 is about the limit for 24/7 charging.
However those who remember the dynamo will remember the equalising charge, very low rate, left on charge 24 hours and topped up after with distilled water. Idea was not all cells are the same, so you over charge some cells so the low cells are fully recharged. This is where the so called smart charger is better than the fixed voltage, as it in essence switches on/off or up/down charge rate, so battery raised to 14.4 volt, then the charger switches off or down, and voltage drops to 12.8 volt at which point it raises the charge rate again, so the voltage spikes do the equalising bit.
Well that is the theory anyway, there is also a school of thought that pulsing the charge can damage the battery, so half a dozen of one and 6 of the other, however my experiment with heavy sulphated battery did show it can take two weeks to recharge, what was a surprise was not gradually over two weeks, but nothing for 10 days, then fully charged in the next 4 days.
The caravan battery now at the house, our normal method would have been to swap caravan battery each time we went up, but since can't use caravan we have both at home at the moment. So 5 car size batteries, 3 smaller ones for jump start unit and mobility scooter, and some small 7 Ah ones from old stair lift etc. So the chargers are always on one battery or another.
I suspect my Kia battery is on the way out,
all other batteries settle down and show a voltage over 12.8 at 0.1 amp, but the Kia battery has been switching between 0.1 and 0.8 charge rate for weeks, after I allowed it to go very low. Or the is some thing left switched on in the car which I have not found.