Quick Search auto filter by selected Customer

Our sales team wants to have the Ship To search on SO Entry include a column for country which isn’t available in the base search. I have a BAQ that includes the columns they want to see but cannot figure out how to get the Quick Search to automatically filter by the currently selected customer so only that specific customer’s Ship To are offered rather than every single one. It seems like this should be simple but I’ve been unable to find anything. So what am I missing?