Twinkly-Eyed Meaning

(idiomatic) happy, of a happy character.

Example: 2012 May 24, Nathan Rabin, “Film: Reviews: Men In Black 3”[1], The Onion AV Club:
  In the abstract, Stuhlbarg’s twinkly-eyed sidekick suggests Joe Pesci in Lethal Weapon 2 by way of late-period Robin Williams with an alien twist, but Stuhlbarg makes a character that easily could have come across as precious into a surprisingly palatable, even charming man.