Disclosure: I'm an engineer who worked in the battery industry for about 11 years.
Specific gravity is the real indicator. To accurately determine full charge you run until all cells are at the specified SG for that battery.
That's fairly inconvenient though, so most of the time you charge until the battery draws less than 1A with a charging voltage below 15V.
You can't rely on voltage. A 10A charger will raise battery voltage to 13.7V before the battery is even half charged.
In the US at least, sealed flooded cell batteries have become somewhat rare. Before about 2006 they were fairly common, but around that time there was a consolidation in the battery industry spurred by serious environmental liability from having battery manufacturing plants, and after that the true "maintenance free" flooded cells all but disappeared. Many batteries say "Maintenance Free*", but when you check the * you find it says "In normal operation", and the vent caps are actually removable. These batteries have some features to reduce water consumption making them likely to give good service without adding water. Like anything else, you'll usually get a longer life if you do check the water.
A trickle charger can overcharge a battery fairly easily. They run a constant 2A regardless of the state of charge of the battery. For maintaining a charge, you either want a float charger, which maintains a voltage slightly above the battery voltage or a timed charger which cycles on periodically, typically once a day, and checks the current draw by the battery when the charger applies a voltage. If the battery draws more than about an amp, the charger remains on until the current drops, then it goes back to sleep.
Older chargers are best used to boost a battery back to the point it can go back into service where the vehicle charging system can finish the charge. If you want to fully charge a battery from a charger, a "Smart" or multi-stage charger is the best option.
There are a lot of decent chargers. I use one of
these to keep the batteries charged in mowers and equipment during the winter. I swap it to a different battery every Sunday so everything is recharged once a month. I use a big Schumacher with boost for bring dead batteries up to usable when I leave a key on or something else happens.
None of this applies to AGM batteries, which are a different technology and have different charging requirements.