Just tell them you were doing handyman/freelance stuff in-between 'official' employment.

'fixing/making XYZ things for friends/neighbors while looking for permanent employment'

You look good for not sitting on your ass during that time and get somewhat of a hand waive pad over that time. If they ask for records, tell them that because it was unofficial, under-the-table work, there's no good records. They're just trying to fill a position, they won't follow up on insignificant data or goose-chases.