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From a slow start to scoring two goals in his dream Old Firm debut, Neil has experienced both highs and lows in recent weeks.
He made a costly mistake that led to dropped points at Dens Park, before Olwethu Makhanya salvaged a point at Tynecastle, bookending a convincing win over St Johnstone.
Now, the national stadium beckons on Saturday, with the season's first piece of silverware within sight.
Rangers' clash with Aberdeen will determine who faces the winner of Sunday's Edinburgh derby in December's Premier Sports Cup final.
For Neil and Derek McInnes' new-look side, they are two games away from ending a three-year wait for a trophy.
Neil said: "You want to play for a club like this and you have to take the good times with the bad times.
"The Dundee [mistake], it's certainly not the first mistake I've made and it certainly won't be the last.
"It's about how you react from it. I'm really enjoying my time here.
"The Hearts match is done now. All we can do is focus on the game coming up on Saturday."
Neil also stressed the importance of winning trophies.
"The full focus has been on that and that [winning trophies] is a big reason why I have come here.
"But to have any chance, we have to win the game on Saturday and that's what we're focusing on."
The midfielder appreciates the opportunity to play more offensively, having been allowed more freedom to move forward since the Old Firm game.
"It differs from game to game, depending on the shape we're playing and if we're playing with two strikers or not," he explained.
"That changes whether I'm closer to them, or part of a more flat two. I'm enjoying both sides of it."
However, Rangers must improve from their performance against Hearts at Tynecastle and avoid the level of play that saw them trailing at Dundee.
McInnes admitted Rangers cannot allow their opponents to dominate as they did in the 2-2 draw at Tynecastle.
Neil acknowledged the team's poor first-half performance against Hearts, saying: "The game on Wednesday night, I thought the performance wasn't perfect.
"The first half wasn't good enough at all. That word control, we didn't have enough until we went 2-1 down, to be honest.
"Then we started playing through the thirds a bit better."
Neil believes the team can improve as the season progresses, but recognises they must win more duels and fight harder.
"I totally agree about the duels and that's something we spoke about at half-time, that we weren't doing well enough," he admitted.
"Over the last few weeks, it's something we've been really good at, which has seen our results turn since Aberdeen away."
Neil is aware of the threat posed by Aberdeen, despite their struggles this season.
"Any team can be dangerous on their day. Aberdeen have got good players.
"It's a bit of a one-off game, because league form goes out the window.
"It's a big chance for them to get into a final too, so league form doesn't come into it. We have to respect their qualities."
Neil and his teammates are focused on winning the semi-final and keeping their dream of silverware alive.
They know they must remain disciplined and continue to improve in order to succeed.
With the potential to secure the club's first trophy in three years, Neil is determined to make the most of the opportunity.
He knows that victory on Saturday could be the springboard for further success and momentum throughout the season.