The new British monarch was on hand for a signing ceremony at the royal residence of Hillsborough Castle in Northern Ireland Tuesday ... where he and Queen Consort Camilla were trying sign some sort of book.

KC3 was having trouble right off the bat ... forgetting it was September 13 and not the 12th as he was putting down his John Hancock. Camilla noted he'd screwed up earlier in the day as well. Just as Charles was pulling the pen back, it started leaking ink on his hand.

He was instantly frustrated, saying he hated the pen ... going on to angrily call it "this bloody thing" as he pawned it off to Camilla, who also noted it was going everywhere before Royal aides came to her rescue.

The King, meanwhile, stormed out ... still pissed over the writing instrument, grumbling to himself that this happens "every stinking time." It's pretty hilarious, just 'cause Charles is usually buttoned up in public. Seems this desk cam caught him in a moment of candor.

BTW, it seems pens and pen paraphernalia might be Charles' kryptonite -- the guy also had a minor meltdown earlier over the weekend when he came across a pen box on his desk as he was attempting to sign a proclamation making him the new top dog ... kind of a big deal.

As he was taking a seat, he frantically motioned for an aide to get all the pen crap out of his way ... and it was all quickly whisked away so he could get to business.