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Brown, 34, initially joined the Yellows on a 28-day loan on Christmas Eve, and will now remain at Cantilever Park until the end of the current season.
Brown has been ever present since joining the club, starting in all five games in the BetVictor Northern Premier Division.
“Scott is enjoying playing and we’re enjoying having him,” said manager Paul Carden.
“He’s been quality for us and we’ll get better the more games he plays and the more the team work with him.
“He’s a great lad, and gets on with the team. He’s enjoying his football and when you’ve got a good player who’s enjoying his football, you get an even better player.”
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