In 1983, with Apartheid coming under significant pressure from both inside and outside the country, South Africa changed its constitution. From now on, not only White people would be allowed to vote!
In 1983, South Africa reformed its constitution to give Coloured and Indian (the latter a very small proportion of the population) people representation in government. We were all now equal. Everyone could vote.
(Everyone except Black people of course, but they weren't considered South African at all.)
Of course, the devil is in the details.
While we were equal, we were still separate. This was still Apartheid, after all. The 1983 constitution created three supposedly-equal legislatures: a White House of Assembly, a Coloured House of Representatives, and an Indian House of Delegates. People voted, but which race your ID card said you were would dictate which candidates you were allowed to vote for and which building those candidates, if elected, would sit in.
In practise, only the Assembly - the White one - mattered. It decided what laws got made, which parties were in power, and which things went into the budget.
The other two were a facade, existing only for show. Even if they had some power on paper it didn't exist in practise.
Did this fool anyone?
It didn't fool many people who were Coloured or Indian. People understood immediately. Turnout rates for those elections were dismal, usually below 20%, and the candidates who ran tended to be exactly the sort of person who wants to hold a powerless position: the pompous, the naive, the corrupt.
A brief aside to discuss the concept of race.
Race is a social construct. It may overlap with some linguistic or biological markers, but ultimately it's something imposed by power. Race is like money: it exists because the people with the guns made it up.
In South Africa, "Black" and "Coloured" are considered to be different races. This loosely corresponds to the traditional divide between Nguni and Khoi people, but "Coloured" also includes a lot of people with mixed heritage (which often goes centuries back - humans don't fit neatly into categories.) If a Black and a Coloured person were to travel to Europe, they would both be considered Black by European standards, but in South Africa there would be a divide, which just shows us how arbitrary race is.
There are, roughly, ten Black people for every Coloured person in South Africa; during the late Apartheid person, which is when the rest of this thread is set, White people narrowly outnumbered Coloured people.