I have just made some.
Suggest you use only the yolk to start with.
Put some warm water in the sink , and stand the bottle of oil in it to warm up ditto the whole egg.
Keep white separate.
I use a stick whisk. 1tsp salt,1 mustard, made or powder, 1 sugar.
I dont add vinegar till end.
Dribble to oil into the egg mix, and whisk well, mixture will emulsify, then you can add the oil a little more generously.
If it gets too thick add in some of the white.
Taste as you go and at the end add vinegar or lemon juice .
Now I have a temp 26 deg so there in no chance of curdling/separating, but in cold UK I always warm oil /egg.