Looking for a Bill Brown from Gisborne

Hi im Crystal and i am looking for my mothers biological father. I don't have much to go on but im hoping there is someone out there who might come across this and be able to help.
It starts with my grandmother Mary 'Puhi' Karora (Carrol) and a young man going by the name of Bill Brown who met at the Hastings Shearing Sheds. Now this would have been in the mid to late year of 1960 that they would have gotten together as my mum was born in September 1961. It was only a brief courtship as to what i have been told as my nan had found a letter in his pocket about his upcoming marriage to someone else. When my nan found out this she left and never said a word about her being pregnant with my mum. So thats all i have and ive asked around and searched the internet but there are so many Bill Browns its just really hard to find the right one. My nan is quite old now and im hoping to find out something if anything as she would be the only person to recognise him if he is still alive.