Hill has been involved in two rows with tournament officials this week, one over match schedules and the other concerning racket restrings. The stringing incident, in which he is alleged to have used abusive language, resulted in a complaint to the Professional Squash Rackets Association.
Should Hill be adjudged to have caused offence, his disciplinary points total could rise above the maximum permitted for the year and he would face a suspension of between three months and a year.
On court, Hill showed his enormous talent by increasingly finding ways of keeping Gough, one of the quickest men in the game, moving and finding holes through which he dropped and drove winners.
Hill plays the second seed, Jonathon Power, for a place in the final. The Canadian beat Egyptian Ahmed Barada 15-5, 15-2, 15-3.
The top seed, Peter Nicol, and the unseeded Stefan Casteleyn, the first Belgian to reach the last four, play the other semi-final.
The Scot had to save a game ball, which could have been crucial, at 16- 16 in the third game before winning 13-15, 15-4, 17-16, 15-9 against the England No 1, Paul Johnson.
Casteleyn followed victories over the world champion, Rodney Eyles, of Australia and the England captain, Chris Walker, with a 10-15, 15-13, 15-9, 17-15 victory against the Australian-turned-Scot John White.