I migrated my site from 1.9x to 2.6.1. I have at least 2 multi select attributes that are not being indexed to catalog_product_index_eav. In researching this issue, I found that if the eav_attribute.backend_type is set to varchar, I should see it in catalog_product_entity_varchar. Its not there, but I have found it in catalog_product_entity_text.
I found this issue by doing an advanced search and realizing that when I selected one of the multi select attributes to search on, no results were found. They do work on my 1.9x site. I have verified all the attribute settings. I've even created a new multiselect attribute as a test and that works fine. I even manually added the non working attribute to the catalog_product_index_eav table and then the search could find it.
So, I'm looking for more ways to debug or other things to check to figure out why its not indexing to catalog_product_index_eav.