Custom post tab content is stored in standard WordPress custom fields.
So every solution that support search in WordPress custom fields can solve this question.
We have tried some plugins which support meta field search, but according to our tests none of them found content accurately in custom meta fields. (E.g. Search Everything, WP Custom Fields Search, Relevanssi plugins).
There is some reliable WordPress plugin that add sophisticated search functionality to your WordPress site using Google, the better search engine in the world. This solution find everything on your site, including content of custom tabs. You can find more information here according to one of these plugins:
We hope one of the plugins we recommend to extend WP built in search functionality to custom meta fields or WP Google Search plugin will solve this question.