Are there specific cache tags which get reset on user login?
No, there aren't any cache tags invalidated upon login. And even if there were, they wouldn't be tied to your cache. Instead, you should act on hook_user_login(), and expire the cache yourself.

Cache invalidation isn't really something you would piggy back onto something non-relevant. Rather, you set up elements with cache tags/contexts etc, and then if necessary you add your own cache invalidation on relevant events.