My father was born in Heemstede on 8th June 1924, he became a South African on 10/9/1952, my mother was born in Haarlem on 6th September 1925, she became a South African on 6/12/1955. I was born on 1/11/1952 in South Africa, am I eligible for a Dutch passport?
Yes, but how easy it will be depends on when your father naturalized.
The relevant Dutch law is: https://wetten.overheid.nl/BWBR0003738/2018-08-01#Hoofdstuk3
If "1 / 11 / 1952" means November 1st, 1952, then Artikel 6.1.i applies as your mother was Dutch when you were born but your father was not.
If, however, "1 / 11 / 1952" means January 11, 1952, then Artike 6.1.f applies as you inherited Dutch citizenship at birth from your father but lost it on your birthday in 1983 (thanks @phoog).
In both cases, you can follow the so-called "Option Procedure" to get your Dutch citizenship.
For 6.1.i (the November 1, 1952 case), you can initiate the option procedure abroad at your local Dutch embassy or consulate following the instructions here: https://www.netherlandsworldwide.nl/living-working/becoming-a-dutch-citizen/option-procedure
For the 6.1.f case (the January 11, 1952 case), you must first legally reside in the Netherlands for a period of one year prior to starting the option procedure. You can find instructions for that here: https://ind.nl/en/dutch-citizenship/Pages/Option.aspx
In both cases, the Netherlands will not require you to give up your current nationality. However, it seems South Africa requires you to first apply to retain your South African citizenship before acquiring a second nationality so you should check carefully on this.