No "log in" button when singleService is set

[farfalleflickan]

Issue Description

When singleService is off, I get the standard login page.
If singleService is on, the link/button to log in is broken/missing, displaying "Log Out" even though I am not logged in. If I manually go to doku.php?id=start&do=login&sectok= I get redirected and can login.
See attached screenshots.
I'm not sure if it's a bug or if I have misconfigured something, looking at the logs I see no warnings or errors and looking at the documentation I don't think I have missed anything.

singleService off:

singleService on (not logged in):

[farfalleflickan]

I did some digging, it is because REMOTE_USER is still set even though we logged out. I crudely hacked in a $_SERVER['REMOTE_USER'] = null; in inc/Menu/Item/Login.php and it works as intended (although whilst fucking up shit, ofc).

I would assume one ought to do it like in auth_logoff, but I haven't managed to make it work...