The moment you start bidding against yourself, you have already lost the room.
The signal I trust most comes from the first reply. A real buyer asks about the name (transfer window, whether the spelling matches, payment by escrow). A chaser answers my price with another price, or opens with "what is your best price". Those threads almost never close, no matter how far I drop.
So I set my walk away number before the first email leaves the building, and I allow exactly one concession. After that the number is the number, and the rest of the thread stays logistics: transfer window, escrow, payment method. Discounting twice in the same thread tells the other side the price is soft, and the third ask arrives about ten minutes later.
Two other habits end the chasing early. I give the price an end date in the same message, so it is a decision instead of an open invitation. And I answer slower than they do; matching their delay is the cheapest tool in the box.
A real buyer who goes quiet for a fortnight and returns with an actual number is not chasing, that is a live deal and I treat it as one. The question is simply who is setting the pace.