I actually found some old posts that suggested that I just duplicate the field and give different access privileges based on the mode. But if there is a newer way in Filemaker 15 I will be eventually getting that and would welcome any comments.
Instead of access privileges, those posts probably suggested setting field behavior options in the inspector.
You could use hide object when to hide one copy of the field when in find mode and hide the other copy when not in find mode.
An alternative to consider would be to put your value list on a global field--possibly inside a popover, and use a script to take that data and perform the find.