The lantern's light can be turned on and off with the "Lantern Implement Lit" toggle on the actions tab of the character sheet.
Allies within the bright light automatically gain the +1 status bonus to perception checks and +1 status bonus to checks to Recall Knowledge (inline rolls must be set up properly with action:recall-knowledge as described in the PF2e style guide).
The counteract for darkness and the secret rolls for environmental hazards, haunts, and secrets are not automated.
The aura in the bright light shows the effect on allies within the aura, but doesn't show on the Thaumaturge (though it exists) to keep effect clutter on the token down slightly.
Adept Benefit
Revealing invisible and ethereal creatures in the bright light is not automated.
Paragon Benefit
The GM secret counteract checks against illusions and transmutations are not automated.
Intensify Vulnerability
The status bonus from the initiate benefit automatically increases to +2 and the creature takes a -2 status penalty to stealth and deception checks while in the lantern's light.