What actually stops The Nester
The badge text is the only first-party rule Dread Forge has published for this threat.
“Close the closet while it's inside. Once it claims a room, stay out of that room or rapidly flash your light at it.”
Read that text as the whole allowed answer: Closets and wardrobes is where The Nester acts, and the rule above names the action that answers it. Nothing in the official text gives a number of seconds, a spawn chance or an audio cue, so this page does not invent one.
5,671 players held the THE NESTER badge at the last reading, which tells you the encounter is common enough to plan for and rare enough that most players have not solved it.