"he has gone to the back gate"
This is correct. The more typical use of gone are as the past participle of to go and would be combined with a form of have to make a perfect, which in this case suggests the subject (he) is still in that state (at the back gate).
There are some times were you will see to be gone (e.g. is gone). On its own, to be gone is used to indicate the subject is no longer present (without specifying where it is)
Is Bob around?
No, he is gone.
Additionally, as FumbleFingers points out there are some fixed expressions like "gone to seed" which function more like adjectival phrases.
As a minor aside, historically an intransitive verb (which doesn't have an object to act on) was sometimes used with to be instead of to have for perfect verb forms ("He is come"), but this is not something you will encounter often and not something that should ordinarily be followed in new writing.