I think he's just acting bored Indy is frustrated having to rescue his estranged father on a grail quest; the very object his dad was obsessed with instead of doing normal dad things with Indy. Any son would be tired and frustrated! Plus his dad never seems impressed with any of Indy's heroics throughout the picture.
Near the end he is definitely more engrossed, as he and his dad start to reconnect emotionally.
Cardboard Box is the Future.

Did you forget Ford was injured for much of the filming of Temple of Doom and the entire conveyor belt fight was filmed using Vic Armstrong (his stunt double)?
Nope. I never got the feeling that Ford was bored at all in Last Crusade. His lively chemistry with Sean Connery would prove that wrong as his energy throughout the tank battle. Ford has even said Crusade was his personal favorite Indy film to work on.

I remember Ford wanted Han to die in either Empire Strikes Back or Return of the Jedi. Of course, he got his wish in The Force Awakens.
Black Sabbath, Judas Priest, Pantera, and My Little Pony: Friendship Is Magic fan

Last Crusade is my favorite. Love the chemistry between Mr. Ford and Mr. Connery

The only movie i've heard Ford not wanting to do was Return of the Jedi. that performance he really phoned in. He's said to have wanted Han Solo to die in the end of Empire Strikes Back, instead of being put in carbonite storage.
"He's dusted, busted and disgusted, but he's ok"

The "no ticket" line was painful to listen to. He was definitely bored with this film, he should have stopped after two.
It sounds like you pick random lines to cringe at. Ford doesn't sound any
less
bored in the other films. And Harrison Ford is
still
on record saying Crusade was the most fun film to shoot.

The "no ticket" line was painful to listen to. He was definitely bored with this film, he should have stopped after two.
"I really wish Gia and Claire had became Tanner" - Honeybeefine

Harrison Ford tends to look bored in his movies. The fact that Harrison Ford is on record saying Crusade is his favourite Indy film underscores that point: he may look bored, but that's just the way he is.

You see I put Last Crusade very far below the other 3 (and yes that includes Crystal Skulls). The plot was the same as Raiders and the performances were horrible (Ford, Connery, Glover, Doody, Elliot, Phoenix and Rhys Davies all dropped the ball big time)
"I really wish Gia and Claire had became Tanner" - Honeybeefine

I guess we all see things differently. FWIW, I put Crusade on par with Raiders from the story to the performances (all of them).
Is very bad to steal Jobu's rum. Is very bad.

He did fine here but his performance indeed didn't feel as energetic as in the first two and the character definitely felt like he took a backseat to his father much of the time.

Ford seemed like his heart just wasn't in it and that's very unfortunate considering he gave a great performance in temple.
"I really wish Gia and Claire had became Tanner" - Honeybeefine

He doesn't seem bored to me at all. He loved working with Connery.
And he's said he had a great time making all of them.