It seems lookup fields are not working in advanced search. None of the lookup fields are searching from the list they are linked with. Lookup fields work fine at other places though, such as object editor.
I tested it on Collective Access demo site as well and found that same problem exists there. I tested with 'Location Where Found' field (element_id=90) on demo site. Originally this field is a drop down list, i changed it to lookup field, it did not work in advanced search form. Restored it back to the drop down list and it worked fine.
I tested for this issue on the following Providence versions:
1.7.6, 1.7.5, 1.7.3 (Demo Collective Access Site)