If it's a custom modal then you can try adding the Condition Builder component in the modal and configure it accordingly. the search icon that you are referring to is called Field Decorators, where through action assignment it is configured.
https://<YOURINSTANCENAME>.service-now.com/sys_declarative_action_assignment.do?sys_id=c6542741ff13101035be517f793bf1bb&sysparm_view=decorators&sysparm_record_target=sys_declarative_action_assignment&sysparm_record_row=1&sysparm_record_rows=4&sysparm_record_list=model%3D15920e6d534723003eddddeeff7b1244%5Etable%3Dglobal%5ElabelSTARTSWITHSearch+For+Record%5EtooltipSTARTSWITHSearch+for+Record%5EORDERBYDESCsys_updated_on
In the action assignment payload definition is mapped and subsequently Event mapping is done. You can try with this approach but I haven't tried it before so can't tell exactly.
