@bbknowles try the following:
| rest /services/data/inputs/all/
You can refer to Splunk REST API Document for Data Inputs
Usually once you open any view in Splunk UI, based on URL in the browser you should be able to figure out which REST API (or endpoint documentation you should refer to).
Could you be more specific about what you mean by data inputs. There are many ways to get data into Splunk, and you won't be able to get information for certain types of data inputs by using REST.
You'll also need to clarify what you mean by "the search behind each input". There is no "search" associated with a monitor type input, it just watches files for changes. There is a search behind db connect inputs, but it's an SQL query, not a search.
In general, I would say you could get some information using REST, but not all information about data inputs.
Is there a specific use case you're trying to address?