The final (hypothetical) routine is below. It is very similar to @cdhowie's first accepted response.
public static bool operator ==(Person person1, Person person2)
{
if (Person.ReferenceEquals(person1, person2)) return true;
if (Person.ReferenceEquals(person1, null)) return false; //*
return person1.Equals(person2);
}
Thanks for the great responses!
//* - .Equals()
performs the null check on person2