Agarwal got hit on his right forearm while batting in the second innings on Day 3; Gill got a cut on his right middle finger while fielding on Saturday.
Siraj had split his webbing during the first T20 International against New Zealand in Jaipur and was out of action since then. He was overlooked with senior pacer Ishant Sharma getting a chance in the opening Test in Kanpur.
Mayank Agarwal and Cheteshwar Pujara were batting on 38 and 29, respectively after India decided against enforcing follow-on despite taking a huge first-innings lead of 263 runs.
When the Patels left their house in the city's Jogeshwari area for New Zealand in 1996, he was only eight years old. In the new environs, he fell in love with the game and worked towards earning a name for himself. "Simply unreal".
The 33-year-old Patel, who had migrated to New Zealand from Mumbai with his parents back in 1996, ended the Indian innings with figures of 47.5-12-119-10 to equal England great Jim Laker and Indian legend Anil Kumble, who had earlier achieved the rarest of rare feat in Test cricket
Kohli was adjudged LBW by the on-field umpire on the fourth ball of his innings though the bat and pad appeared very close to the ball.
Shubman Gill while playing a shot in the ongoing second Test against New Zealand in Mumbai
Ajaz Patel scalped took a 10 wicket haul at an economy of just 2.49.
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Playing in India for the first time, the 33-year old, who had moved to New Zealand at the age of eight, turned it around for the visitors after a strong start by the Indian openers.
The 22-year-old Gill scored 44 runs off 71 balls, missing out on the opportunity to get a big Test knock under his belt. He was dismissed by left-arm spinner Ajaz Patel, who scalped all the four Indian batters on the day.
Agarwal, who has been in and out of the squad in recent times, scored a fine 120 under pressure on the opening day of the second Test before which he watched legendary Sunil Gavaskar's batting videos and slightly changed his stance.
Agarwal (120 batting, 246 balls), who is all but certain to sit out once Rohit Sharma and KL Rahul come back during the next series (if South Africa then away, if West Indies then home), added to a happy headache for coach Rahul Dravid, on a day when vice-captain Ajinkya Rahane had to be "dropped" because of a hamstring niggle.
The BCCI and the team management found an "exit route" which was honourable for both the distinguished senior cricketers as everyone associated wanted to be subtle while taking a tough decision, at least for this Test.
Tom Latham will lead the side in place of Williamson, who has been dealing with the tendon injury since it first emerged in the New Zealand home summer.
The match is expected to start later Friday amid wet weather.
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Mumbai is witnessing heavy unseasonal rain which has caused a sharp drop in temperature. The overcast conditions would bring seam and swing bowlers into the equation due to underlying moisture content.
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