Elsewhere, soreness around Trent Boult's pelvis and left hip prevented him bowling with the second new ball on Saturday.
He will travel to Wellington where his fitness will be monitored. Tim Southee is expected to return regardless, on a more seamer-friendly pitch. If Boult does not pass muster, Matt Henry is next in line. The toughest decision for coach Mike Hesson and captain Kane Williamson is which spinner to omit - presuming they play one rather than two on a surface usually suited to pace.
Mitchell Santner has been the incumbent because of his all-round talents but Jeetan Patel is challenging through his guile and ability to take the ball away from the South African top seven's three left-handers.
The 36-year-old took two for 72 from 36 overs in the tourists' second innings. He earned a fourth consecutive international dismissal of Quinton de Kock, and Elgar miscued a lofted drive which found Williamson at deep mid-off.
Patel was brought back for the one-off test series in India, having devoted himself to English county Warwickshire for a few seasons.
He has since played Bangladesh, Australia and South Africa, and looks an integral part of the New Zealand side heading to June's Champions Trophy.
"Taking the ball away from the left-handers is a nice option to have," Black Caps captain Kane Williamson said of Patel. "And drifting the ball against right-handed batsmen is threatening as well."
South African captain Faf du Plessis said Patel was tougher to play in the circumstances.
"Spinning the ball away [Santner's left-arm orthodox stock ball to the right-hander] is normally more of a threat, but in this match, there was a lot of rough created by the left-armers and he [Patel] was consistently there."
Patel has not played any of his 22 tests at his home venue.
"I'd love to play a test at the Basin. I have played a lot there so I tend to know what's going on. We have to decide what it looks like, and how we can best attack. Maybe I get picked to get Quinton out.
"I know I am not going to be in this team forever, so I am enjoying every moment. They are going somewhere with their cricket and I want to help them get there."
Seeing Patel bowl had encouraged du Plessis to push for a second spinner to be flown out to join Keshav Maharaj, who took five for 94 in New Zealand's only innings.
"We've been surprised. New Zealand conditions have changed since we were last here [in 2011-12 for tests]."
Meanwhile, Broom's selection is on the back of his 424 runs at an average of 53 in the Plunket Shield.
The 33-year-old received a call-up in December for the ODI squad to play Bangladesh after a six-year hiatus.
He left the second year of his English county contract with Derbyshire to rekindle his international dream.
Dean Brownlie was not considered due to the injury he suffered in an outfield clash during the ODIs against South Africa. He missed Northern Districts' match against Central Districts at Seddon Park as a result.
The 32-year-old has scored 321 runs at an average of 40.12 this first-class season and was on standby for Taylor's eye issues during the Pakistan series, despite having rebranded himself as an opener.
Of the other contenders, Auckland's Colin Munro has 475 first-class runs at an average of 95, including three centuries; and Central Districts' Tom Bruce has 473 runs at 59.12, including two centuries.
"We wanted someone with plenty of playing experience, someone who plays pace well, and someone who had the advantage of seeing South Africa earlier in the month," Hesson said.
