You have the following options to search In External List.
- Create a
Content Source to get data from
External Content Type.
- Create a
custom Search Scope with
Search Core Result Web Part to get data from a specific list
- Create a custom search form via Jquery.
(1) Create Content Source to get data from External Content Type
select "Business Data Connectivity Service" > "Crawl selected external data source" > Click on Ok.
Go to Central Administration > Application Management > Manage service applications > Search Service Application > Queries and Results > Scopes.
Now Next, create a new page. Add the following 3 webparts:
- Search Box
- Search Core Results
- Search Paging
In search core result add ur scope.
For more details check Search Scopes within BCS Data
(2) Create a custom Search Scope for your List.
Instead of creating a content source for external content type, you can create directly custom scope for your list.
Check the detail steps at Create a Search Scope for a Sharepoint 2010 List or Library
(3) Create a custom search form via Jquery
Try to create a custom search form via Jquery as the following:
Check the detail steps at :