Mustard will make it better but you don’t need it.
You won’t get as good an emulsion and it will separate faster. Once you pour it on some salad it will be pretty hard to notice that.

If someone is at the point in their cooking journey where they’re asking how to make vinaigrette, I keep it as simple as possible. TBH even the pepper isn’t strictly necessary. Many people don’t have pepper grinders and preground pepper doesn’t add much flavor.

Salt is the only one that I’d say is absolutely necessary.