Byrnes is the latest trialist to arrive at Vale Park, with Valiants boss Lee Sinnott currently also running the rule over Andy Smith and another Australian, Matt Deegan.
Sinnott told the club's official website: "Mark has been recommended to us and so we will be taking a look at him to see if he can add something to our team.
"Unfortunately the weather has disrupted training yet again, so we can't really put a time limit on it as we need to get a good look at him and of course the other two lads."