Can the pocket dimension created by the mirror of life trapping be returned to by using the Gate spelll?

A wizard needs a few decades to think over a problem, and decides to do so in his mirror of life trapping to prevent himself from aging. He packs a bag full of writing supplies and a 5000gp diamond, and has a servant activate the mirror to trap the wizard inside. After a few years have past, the wizard realizes he misses his liquor cabinet, and casts Gate to return to his study. After grabbing a couple bottles and regaining his 9th level spell slot (he took too long and the gate had run its duration), he wishes to return to the mirror. Can the wizard recast gate and step back into the mirror, or must he return to the mirror by his servant reactivating the mirror? Does the extra dimensional cell remain in existence when the wizard leaves it, or collapse until the cell is refilled? What if the wizard leaves his notes, are they ejected when the wizard leaves?

If applicable, what other pocket dimension can or cannot be returned too in this way?