Follow selected file in version control history view?

You can use "Git (or another VCS) | Show History" from the context menu of a file. You can assign a shortcut for this action in "File | Settings | Keymap" or use "VCS | VCS Operations Popup" that has its own shortcut.

Thanks for your reply and hints.
I guess the simple answer is there's no such feature, right?

No, only diff markers from the last commit are shown in the gutter automatically.