(verb) To walk around wearing a shirt but no pants or undergarments. Synonym of Donald Duck. Technically applies to men only, but plumbing issues aside, easily applies to women, too. Sometimes a mild pejorative, implying imcompleteness or an unwillingness to commit.
"It's so beautiful out, I'll think I'll shirtcock today." (verb form)
"There sure were a lot of shirtcockers out on the playa this year." (noun form)
"When Mozart died, he shirtcocked his 'Requiem.' Someone else had to finish it." (verb form, implied meaning)
"Annaconda, quit shirtcocking and just pick a place to eat!" (verb form, implied meaning)