Toum is a valid condiment and is naturally vegan. To make mayo vegan you need to do weird things with unpalatable/indigestible waste products. But mayo isn't a very good sauce anyway.
Hidden Valley makes a plant-based ranch, if you wanna go that route. The vegan mayo I use is from a brand called Best Foods. I think it's just a regional rebranding of another mayo. It's ok but if you are recently coming over to the vegan lifestyle, it is noticeably off from real may. It works well as a spread of for an ingredient for a sauce though. I have a non-vegan friend that was raw dogging her chicken nuggets with it though so ymmv.
I see your Toum and I raise Yemen's Zhug: another absolutely banging middle eastern condiment. It's easy af to make, you can decide how spicy you want it, and it rips. I put it on basically anything.
Happy to be of service. Zhug by itself is a pretty strong sauce so you use small quantities of it, but you can make it into more of a dip by mixing it with about two parts of yoghurt (vegan yoghurt works fine too).