Now the pair have been reunited at Goodison Park, McNeil is starting to show that he could be a key figure in Everton’s fight against relegation, with his early goal earning a precious three points against Brentford last time out.
Dyche said: “I think he’s just finding his feet again. It’s a big thing for a player who came into a smaller club like Burnley.
“It’s sometimes an easier place to go when you’re young. He built a very good reputation and gets a move here and it becomes a bigger feel. I think he’s just got his shoulders back.
“We reminded him that, when he relaxes and works hard, he’s a good player. The information given to him has been very, very simple. I think he’s a player who’s ready to improve and he is improving.”
With Dominic Calvert-Lewin still sidelined by a hamstring problem that has dogged him all season, Everton remain very short of options up front, so Toffees fans will be hoping McNeil can chip in with more goals.
“I’ve spoken recently about the whole team being goalscorers, or having the mentality to score goals,” said Dyche.
“That has definitely improved, the amount of bodies getting in the box but the intent, the body language. It started with the set-pieces, then you build that mentality into playing and that freedom – I call it the bliss to miss. Be in there to score.
“If Dwight can chip in, that’s great, but I’m not just going to single out one player, it’s about all the players.”
Dyche has overseen three home wins that have lifted Everton out of the bottom three since taking over the hotseat but has picked up only one point away.
He takes his side to Chelsea on Saturday, with the pressure on Blues boss Graham Potter having been eased by three straight wins and progress in the Champions League.
Dyche said: “I know Graham a little bit. He’s gone into a new situation. I know they’ve spent fortunes but you’ve still got to mould them into a team. Sometimes it’s hand in glove and it works straight away and sometimes it takes time.
“Whatever everyone was looking at and thinking, and still maybe are because there’s still a few ups and downs, at the end of the day they’ve got some very, very good players, and very strong players.
“It’s another tough away game but we’ve got to be ready for that, and I think we’re showing in our mentality we can be ready for that – whistle blows, we’ve got to deliver.”
With British managers of Champions League clubs very much a rarity, Potter is under particular scrutiny, but Dyche hopes the tide could be turning.
“It’s been there for a long time, that kind of feeling,” he said. “I don’t think it’s relevant to English, British against foreign managers – if you’re good, you’re good; if you can do the job, you can do the job.
“I think the breakthrough would be an English manager winning the league or something like that. But there’s been lots of good signs from English and British managers. I respect Graham, I think he’s a good guy as well as a good manager.”