You become undetected from the map when:

• You are in light level 3 or less (i think) – such as a dark cave, or a dark base
• When the player is in a different dimension (their head will instead show up on the nether/end map)
• You drink invisibility potions – these last at maximum 8 minutes, which is how most players say hidden

That being said, you can use this to your advantage when building a base somewhere. When making an underground area to hide all of your valuables, don’t place any light sources, place slabs so that monsters can’t spawn, and increase your brightness settings. Its by far not very convenient, but it will hide you from the map as well.