Logs my servers IP address

You need some other plugin.
For example Simple login log. I’m not tested it. Just first found.

I just tested that plugin and it does log the correct IP address, but now how do I get fail2ban to see those logs.

Wait… I can’t understand. Do you want to block each user? Even succesfully authentificated?

No I want to block failed login attempts.

But what you need to get?
Record all users logins to system log?
And fail2ban must catch only invalid attempts and block source ip?
But successfull records for what?
“Simple login log” record all attempts. You may export records as CSV file.
Or you need to change source code of wp-fail2ban plugin.

Problem is fixed, I’m using varnish cache on my server and it was not showing the IP address from the user trying to login. I installed a module called mod_rpaf onto my server and now its logging the correct IP addresses.

Now I understand! ?? Of course. Varnish or Nginx can hide external ip address.