Recruit Gunston and defender Rich won't face the Swans at the Gabba on Friday or play in the Lions' VFL team, Fagan revealed on Thursday.
Instead they will be placed in a training block indefinitely after the coach said the pair approached him on Monday.
"Both those guys aren't going to play this week and they're not going to play for a little while," Fagan said.
"They're not happy with the way they're playing at the moment; they believe their form doesn't warrant selection.
"Goes to show you what good and honest men they are."
Gunston, 31, has averaged a goal per game in 11 outings since arriving from Hawthorn, but has gone goalless and tallied just 11 disposals across his past two starts.
Defender Rich, 33, has battled niggles and was subbed off during last week's loss to Hawthorn.
"There's obviously the option to go back to the reserves, but at their age the best thing we can do for them to get back to playing their best footy is to give them a training block," Fagan said.
"For the next few weeks, that's what they'll be doing, building their bodies up, building their fitness up, and hopefully in a few weeks' time they're feeling really good.
"What happens is they end up not training and it doesn't help them.
"So we want to do a circuit-breaker with them … I'm not sure how long they'll be out for or when they'll be ready to come back.
"So when you see the team tonight they'll be out 'managed', which is one of the great words that's just appeared in recent times."
Jaspa Fletcher, the son of former Lion Adrian Fletcher, will make his debut for Brisbane, and Kai Lohmann will play his first game of the season. Darcy Fort and Ryan Lester will also return.
Keidean Coleman is back in the starting 22 after acting as the substitute last week, but there is no room for Dayne Zorko after the veteran served his one-match suspension.
Sydney have lost important pair Lance Franklin and Isaac Heeney to injuries, with gun midfielder Luke Parker back after his suspension, and mid-season recruit Jack Buller to debut.
Brisbane are 8-4 and clinging to fourth on percentage after consecutive losses. All four of their defeats have come on the road.
Booming left-footer Rich was a 2021 All-Australian and has been a Lions fixture since 2009.
Triple-premiership Hawks forward Gunston was recruited as a replacement for Daniel McStay, but has kicked 11.9 this season and managed just one goal in his past four games.
"He's disappointed in himself; he's a very honest person and a proud man," Fagan said of Gunston.
"For him to come in and have a chat about it is outstanding.
"Both of us are optimistic that he can get back to his best form.
"He just needs to be moving a little better than he is at the moment."
