An unlovely combination of a 'tit' and a 'fuckwit'.
Rarely used in jest, say it when you mean it.
Irish in origin, perhaps, but widely used in the more educated areas of Liverpool, i.e the south-end or town, to describe the evil and stupid little cunts who live in the filthy north, especially around County Road on match days.
'Eh! Gobshite! Put your sister down and get back in the shed!'
The lad's a gobshite, good for fuckall, let's kick the living stink out of the prick.