The decision to enforce the follow-on is made by the captain of the team who batted first, who considers the score, the apparent strength of the two sides, the conditions of weather and the pitch, and the time remaining.
This contrasts with the order of innings batted in the First Test of the same series, where Indian captain Virat Kohli had the right to enforce the follow-on, but declined.
Law 14 of the Laws of Cricket[1] considers the length of the match in defining the minimum lead required for the defending team to enforce the follow-on: When the start of a match is delayed by one or more full days, e.g., due to bad weather, the score lead required to enforce the follow-on is reduced accordingly.
In his classic text The Art of Captaincy, Mike Brearley deals with the issue in a single paragraph, and finds the advantages overwhelming.
For their part, Australian captains Steve Waugh and Ricky Ponting were also notably reluctant to enforce the follow-on, although that was perhaps more to do with wanting to allow Shane Warne to bowl on a deteriorating pitch later in the game.
Michael Clarke only enforced the follow-on once in his career as a captain (during his final match in the 2015 Ashes), even when holding a substantial first innings lead due to the risk of tiring his fast bowlers.
In the first innings of the First Test at Sydney, Australia had scored a massive 586 (Syd Gregory 201, George Giffen 161) and then dismissed England for 325.
But heavy rain fell overnight (in this era, pitches were not covered between days of play), and the next morning, England's slow left-arm bowlers, Bobby Peel and Johnny Briggs, were unplayable on the sticky wicket.
This started out very badly: Australia scored 401 (John Dyson 102; Kim Hughes 89; but Botham took 6–95), and asked England to follow on after bowling them out for 174 (Lillee took 4–49; Lawson 3–32).
Matters did not improve: Geoffrey Boycott and Bob Taylor soon followed, and with England 135 for 7 and still 92 runs behind an innings defeat looked likely.
The only other bright spot for India was the bowling of Harbhajan Singh, who took 7 for 123, including a hat-trick (Ricky Ponting, Adam Gilchrist, Shane Warne).
Laxman came to the crease just before the end of Day 3 and proceeded to change the course of both the match and the series by hitting 281, at that time the record for an Indian Test batsman.
India progressed to 657/7 in their second innings (a lead of 383), declared shortly before lunch on the final day (giving Australia insufficient time to reach the total, thus securing at least a draw).
Neil Wagner was the catalyst with a short-ball assault during the afternoon session, and he capped the comeback by taking the final wicket amid rising tension at Basin Reserve.
New Zealand's first innings ended at 209 with a rear guard action from Tom Blundell and Captain Tim Southee limiting the damage to a 226 run deficit.
Controversially, the ball prior should have been called a wide, as a bouncer flew well over the batsman's head, and one run extra could have potentially seen the match end as the third ever tied Test.