If you look at the Analytics server call (filter calls by b/ss) in the debugger, you will notice query parameters like 'pe' and 'pev2'.
pe determines the type of link. For custom link it is 'o', for exit link it is 'e' and for download link it is 'd'.
pev2 determines the type of link name.
So in case of Exit link call, if you see pe: lnk_e and pev2: some name, then the exit link call is firing on the page.
Document Reference: https://docs.adobe.com/content/help/en/analytics/implementation/validate/query-parameters.html
Hope this helps!
Thanks,
Saumya