select_advanced search in custom fields of custom table?

I have a CPT A with custom fields 'first_name' and 'last_name'. They are stored in a custom table.

I have a different CPT B, also stored in a custom table, with a custom field that selects a post from CPT A via a select_advanced. CPT A has no title, so if I search in the select_advanced of CPT B I only get a result when I type 'Auto Draft'.

I already added a rwmb_{field_id}_choice_label filter so it shows the correct labels, but I can't search in them.

How can I change the select_advanced search box so I can search in 'first_name' and 'last_name'?