Has verb3 or Has been verb3

Has + past participle (what you're calling Verb3) is the present perfect.

Is + past participle is the passive.

(They can be combined: has been + past participle is a present perfect passive.)

But only transitive verbs can use the passive, so is gone and has been gone are not possible verb phrases.

However, many past participles can also be used as adjectives, so is gone and has been gone are grammatical, but not as verb phrases: they consiste of the verb is or has been and the adjective gone.

So, both of your sentences are grammatical, though they are structurally very different (gone is a verb in the first, and an adjective in the second). The first says that at some point the light stopped being there (verbal); and the second says that over some period the light was in the state "gone".

Idiomatically, the second is much more natural than the first, for just this reason. The event referred to in "the light has gone" is an event which finished at a particular point, and this is incompatible with "for a while", which denotes an interval of time, not a point.

"The light has been gone", on the other hand, refers to a continuing state of affairs - the period during which the light can be described as "gone", and this is consistent with "for a while".