Getting a quick search onto Quick Search Tab

We have a quick search that allow users to display Customers
where the criteria is whether customer contacts are active
or inactive. While the quick search shows up on the Quick
Search tab for Sales Order's Customer search button, it does
not show up on Quote's or on any other Customer search's Quick
Search tab. But it always shows up as a right-click quick search.
Similar issues have happened for other quick searches.
Unfortunately our users like having Quick Search available on the
Quick Search tab, not just right-click.

For this quick search, the Return Column and Context Key are
Customer.CustID, and the baq has BAQ Search "Like" Columns of
Customer.CustID (later I added several more out of general
paranoia e.g., Customer.CustNum). I also tried making a
duplicate quick search, starting from Quote form's Quick Search
entry, but it again showed up on Sales Order's Customer search's
Quick Search tab and not Quote's.

Any help would be appreciated. We are using version 9.05.604A.

Thanks,
Tracy

Restek Corporation