I've been reading through this excellent answer to understand how pg_trgm works a bit, but I'm still unclear on the most efficient way of solving this query (efficient in terms of speed of search):

I have a table search that I run trigram searches on that looks like this:

Column      |  Type   | Modifiers
------------+---------+-----------
id          | bpchar  | collate C
user_id     | integer |
type        | text    |
search_on   | text    | collate C
data        | json    |
Indexes:
 "index_search_id" UNIQUE, btree (id)
 "index_search_search_on" gist (search_on gist_trgm_ops)
 "index_search_type" btree (type)
 "index_search_user_id" btree (user_id)

In this scenario, user_id is NULLable and type is also NULLable. The queries I'd run amount to these possibilities:

1. Search for rows WHERE user_id = 123 OR user_id IS NULL AND search_on % 'mystring'
2. Search for rows WHERE user_id = 123 OR user_id IS NULL AND type='my-type' AND search_on % 'mystring'

In plain words, I want all rows that have my user_id or NULL user_id, optionally are categorized by type, and match the term being passed in.

Right now I just have individual indexes on the 3 columns (as shown above) that can change based on the query. I understand however that a single index is generally more efficient.

Is it possible to use a single index that does trigram searches, but also exact match on user_id and type where they can optionally be NULL.