Searching using Search Services
One way to find more directories and search engines is to just search for them! Try it. One search engine won't keep you from finding references to others, or to sites with lists of links to a number of searching sites.
Search as a service is a branch of software as a service (SaaS), focussed on enterprise search or site-specific web search.
The most popular search services are always advertising. It's easy to find them. But there are lesser-known, smaller ones that may have found and indexed sites or documents that may be the ones to match what you are looking for even one,
for example, that only catalogues universities' archives of historic documents.
Most of what you need to find day-to-day can be found in the larger search services--but if they don't have what you need, don't hesitate to search for ones that do.
The need for search
Searching is an important part of any business database function, either through internal databases, internal document stores, or through the content of a website. This is needed for both internal company staff and for external customers.
Although a simple database query such as "List existing customers with a postal code for Argleton" is a trivial piece of in-house software development, probably through SQL, this is a simplistic example. More complex searches such as
"Find all product brochure text that references the Bindeez product" or "Search the customer-uploaded reviews for any synonyms of 'caught fire' and 'pets' or 'children'" are more difficult to implement.
Search, especially free text search or text searching through images of scanned documents, is a specialist discipline.