It's interesting that going first in negotiation is often seen so negatively, but most of the actual research I've seen indicates that the anchoring effect of going first outweighs the disadvantages.
Ideally you string them along while on speakerphone, and engage in some sort of necessary, but low-mental-effort work you've been putting off.
I've done this as well, but not quite as successfully. 'hold on a minute, let me go find my wallet...' <mute> 'hm, it wasn't upstairs, let me go check my car' <mute>
I'm curious how that ends up in reality.