The concept of searches could completely mirror the filter concept:

a) user clicks on "init search" button, enters search criteria", clicks on
"apply search" button. Another button to "search next" might be useful (or reuse
"apply search" button for that). Search would always start with current record
and wrap around.
b) field with "autosearch" attribute, just like "autoquery" (or "autofilter"??)

GFForm functions: init_search, change_search, discard_search, apply_search.
Additional GFBlock function: search (for direct use in triggers).