There isn't a built-in feature/tool to achieve this result.
But you can do it manually by placing two mirrored symbol instances side by side so when you draw in one of them the other one will be updated with the same drawing but inverted horizontally or vertically.
You can also use a mask inside of the instances if you don't want overflow.
Thanks JC, that's a good workaround I hadn't considered.
Whats the reason for not having brush symmetry available?