"It hasn't gone his way just yet but I don't have any doubts it's around the corner for Tim," Wright said.
"He's working extremely hard in the nets on his technique. Hopefully the next pitch we go to is going to give a little assistance for him."
Skipper Ross Taylor was more cautious.
"Tim didn't have the game of his life," he said last night.
"He struggled a little bit with his action but he's played a few tests now. If he does play [in Hamilton], hopefully he can bowl a bit better than he did in this match."
Wright and Taylor described Southee as a "confidence player".
Taylor, asked if he leaned towards having Southee as part of his second test squad to be named this afternoon said: "We'll just have to wait and see."
Wright stressed Southee's value when the pitch was grassy - citing the snooker-table green strip in Hobart in December when Australia were beaten by seven runs. New Zealand's hope is there is more in the Seddon Park strip for the bowlers than Dunedin offered for the first test.
"If Tim has that bit of grass on the pitch, as there was at Bellerive [Hobart] he's a bloody good bowler and very effective," said Wright.
"I don't have any personal worries about him. I've just got to keep him up and about. He's a likeable character, pretty loud in our dressing room. So he's a pretty important part of it."
Wicketkeeper BJ Watling, who missed the Dunedin test with a hip irritation, is also out of contention for Hamilton for the same reason, while middle order batsman Dean Brownlie won't make it either.
He is recovering from a fractured finger and is to play Canterbury's next Plunket Shield game against Otago next weekend with a view to being in the frame for the third test in Wellington, starting on March 23.