Tested (25.03.2024): should just work if added to the searchFields (with TYPO3 v12 and v13):

mod.linkvalidator.serachFields.sys_file_reference = link

Since TYPO3 v12, linkvalidator also checks fields if type = "link".

Reproduce¶

1. Change default page TSconfig for linkvalidator to include sys_file_reference:

mod.linkvalidator {
    searchFields {
        pages = media,url
        tt_content = bodytext,header_link,records        
        sys_file_reference = link
    }

...

}

2. Create a "text & images" or "text & media", add an image, add a dead (not existing link) in the "Link" field for the image metadata.

3. Restart "Check link", the dead link should now appear in the Reports

Results¶

Clicking the pen will jump to the edit wizard for sys_file_reference, but you can't change the link there, you need the edit wizard for tt_content.

So, Linkvalidator does not properly handle sys_file_reference records (and probably wasn't intended to because it was developed before FAL).