I thought a booking deposit was a refundable, but not unsubstantial amount payable to an EA in order to secure 'sale agreed' status? In my experience it was a sum paid pending the survey and other preliminaries, but which could go back to the potential buyer in the event that the sale agreed status falls through.
For example, my place went sale agreed recently, and the potential buyer paid €5k to the EA as a booking deposit. Within some weeks, it became unlikely that the potential buyer's house would sell within a reasonable period of time and with my consent, the EA repaid the booking deposit and the house went back on the market.
Does the OP's vendor want the non-refundable 10% (or whatever %) deposit agreed with the aim of copperfastening the sale?
Maybe I've got that all wrong?!