Test::TCP is a module for testing TCP connections. WWW::Mechanize::PhantomJS does not use Test::TCP, so the two are not interrelated. I think Test::TCP is pulled in by LWP::Protocol::PSGI for self-testing.

There may be problems with your setup that prevent Test::TCP from passing its test suite that may also prevent WWW::Mechanize::PhantomJS from working, but they are not apparent to me.