Perhaps from a nasalised variant of Scots begeck (“to deceive, disappoint”), equivalent to be- + geck.
begunk (third-person singular simple present begunks, present participle begunking, simple past and past participle begunked)
- (transitive, dialectal, chiefly Scotland) To befool; deceive; balk; jilt.
begunk (plural begunks)
- (dialectal, chiefly Scotland) An illusion; trick; cheat.