You cannot use a hidden tracking pixel on Facebook. It will simply not work due to Facebooks extensive privacy platform.
As an example Facebook will download the pictures through their own proxy, cache it, and serve this cached version to the Facebook users.
Your server's logfile will never get the IP, user-agent or other headers from the user. Instead you will get Facebook's own IP.
I think your only option is to lure him out of Facebook with links.
Then you can have your hidden tracking pixel on some message board, or other place with less privacy security than Facebook.
Also forget about sending those hidden things in emails. It is a standard-setting in most email clients to block "retrieval of external files". For this very reason.
Good luck
