Are long-term farm dwellers allowed to keep livestock?

The long answer

If you are living on the farm that your grandparents worked on since 1988, but are not working yourselves for the farmer, you would be known as “farm dwellers” which is not the same as farm workers, who are actually employed by the farmer. There has been a long history of conflict between farm owners and farm dwellers over grazing rights and livestock numbers.
To give the background: in 1997 the Extension of Security of Tenure Act 62 (ESTA) was passed. This law applies to both farm owners as well as farm workers and farm dwellers, and was meant to balance the rights of farm owners and farm workers and dwellers. Section 6(2) of ESTA lays down certain rights for farm dwellers, including access to water, access to and from the farm, and the right to receive bona fide (genuine) visitors.
In terms of ESTA, if you have lived on the farm for longer than ten years, are older than 60 and can no longer work on the farm, you are entitled to stay there for the rest of your life. You can only be removed if you have intentionally harmed another person living there, or damaged the farmer’s property, or helped unauthorised people to move onto the farm and build dwellings, or broken one or more of the agreements you have with the farmer, and have not complied with it after being given a month’s notice to comply.
But that security of tenure does not give you an automatic right to graze livestock on the land. Keeping livestock is a separate tenure agreement with the farmer or landowner. So even if you had security of tenure on the farm, you might not be able to make a living there.
If you were employed on the farm and you were dismissed, meaning that your employment relationship had ended, you could be evicted with 12 months to vacate the farm in terms of ESTA. ESTA does not stop evictions from happening, but lays down the rules for a legal eviction to happen. To be legal, an eviction can only happen with a court order and the court must take into account all the relevant details before granting an eviction order. The municipality must also be informed so that they can offer alternate accommodation to prevent homelessness. 
But because the farmer has so much more power than the farm worker or farm dweller, and because many farm workers or dwellers don’t know their rights, and enforcement of ESTA has been weak, there have been many more illegal evictions by farmers than legal ones. 
It could also be that if you were not allowed to keep livestock and so could not make a living, you might have no choice but to leave the farm, and then the farmer could say that you left of your own free will and were not evicted. This would be called a “constructive eviction”.
In terms of ESTA, farmers have to give a notice period for the farm dweller before they can impound livestock, but many farmers have also impounded livestock illegally and sold them.  
If the farmer can prove that you are grazing more animals than the area can support, he can get a court order to remove the livestock. In 2020, the Farmer’s Weekly reported a case where the landowner had gone to court after getting a Veld Condition Assessment Report from the Mpumalanga Department of Agriculture, Rural Development, Land and Environmental Affairs, saying that there was severe overgrazing and extensive damage to the grazing in a designated area. The Report was drawn up in terms of the Conservation of Agricultural Resources Act 43 of 1983 (CARA) which requires landowners and users of agricultural land to use land responsibly and not overgraze. The court order was granted for the landowner to remove the livestock.
All in all, it might be difficult to get the landowner to agree to your 35 cattle. ESTA does provide dispute resolution steps through mediation and arbitration, where the idea is that the parties come to some sort of agreement, but in practice, there has not been much support from government agencies to use these mediation and arbitration steps rather than going to court. 
Perhaps you could approach an organisation like the Association for Rural Advancement (AFRA) for further advice:  
Email: afra@afra.co.za

Wishing you the best,
Athalie