Coinciding with the current series between the two countries, there is an excellent
in-depth piece over at Cricinfo from Kanishkaa Balachandran looking at the role India played in helping South Africa gain re-admission to the international arena:
Such was India's influence that Pakistan fell in line and West Indies eventually seconded the vote after India pushed for it. According to Majumdar, there was a sense of urgency to promote the new South Africa through cricket and not any other sport. Had it not been for the ICC meeting in July, South Africa would probably have made their official re-entry into international sport through the Barcelona Olympics in 1992, missing the cricket World Cup in 1992.
Well worth a read.