WP Extended Search is a lightweight and powerful search plugin.

With this plugin you can customize WordPress search to search in Post Meta, Author names, Categories, Tags, or Custom Taxonomies via admin settings. You can control the default behavior of WordPress to search in the post title, post content, and post excerpt.

Apart from customizing default search behavior, you can create multiple search settings, and then you can assign these settings to custom search forms.
For custom search forms, you have the option to choose from a widget, shortcode, PHP function, or HTML.