Are there equal opportunities for near native English speakers to get an EFL job anywhere in the world?

Answer 1

How near native? If you are almost accentless then keep your origins private and you'll have no problems. If you cannot do this, just say you immigrated to (?) when you were very young/or started learning English very young. This was the case for me and I've never had any problems; and in fact 99% of people I meet don't realize that I wasn't born in Canada (I immigrated at 15 but started learning English at 4)

Answer 2

A lot of countries require a TOEFL score if you're not a native speaker; but, if your English is flawless and you've got citizenship (or residency even) of an Anglophone country, then you can probably hide your origins.