What situations trigger the Master Sword's special power?

I know the following situations activate it:

• Being anywhere inside Hyrule Castle or a Divine Beast
• Fighting any of the full-size guardians (fighting the smaller scouts inside shrines will not activate it)

I know that "calamity goop" does not activate it.

According to the Zelda Wiki page on the Master Sword, the Master Sword should glow under a number of circumstances (emphasis mine):

The Master Sword has a base strength of 30 damage; however, its holy power is awakened in the presence of evil. While Link is inside a Dungeon or near Guardians or Malice, the blade glows with a blue aura. In this state, the Master Sword's power is doubled to 60.

Thus, the Master Sword will enter its awoken state when:

• When Link is inside a Dungeon (any Divine Beast or Hyrule Castle)
• When fighting full-sized Guardians
• When fighting certain enemies affected by Calamity Ganon's Malice (as Mage XY pointed out in the comments, certain enemies who are technically affected by Malice may not awaken the Master Sword eg Silver Lynels)

There are also certain effects on the Master Sword's durability and abilities when awakened, but this information can be found in greater detail in the Master Sword wiki entry.