This is potentially a catch 22.
Under normal conditions a great many on this forum would advise not to go anywhere as that usually means you have forfeited the house to the person staying.
But in this case I wonder if she is being straight with you or is she planning to be dishonest with regards to “while she packs”. I have questions that I would ask myself in this situation.
Is she trust worthy enough to be left alone in the home? IE will she only take what is rightfully hers, so that I won’t have to file a court order to get something back?
Also, once the month is up can you trust her to leave without incident? Will you have to go to court to get an order to enforce the agreement in which she agreed to leave with only her belongings after the month was up?
This is something that only you can decide, you know her better than any one. Another consideration, is she in an emotional state that she is potentially in “I want to get even” mode, or is she in a position where it literally is simply a case where she does not want to be around you while she packs, and she just wants to make a clean exit?
Then you have to ask yourself, if you do not sign will she get nasty and make your life miserable?
Good luck, keep us posted, we’ll be willing to offer our experiences and advice when needed.