The finished sauce should be uniformly glossy and about the consistency of bottled Catalina dressing or heavy cream, but the more butter you add, the thicker it will be. For a more wine-tasting sauce, use the lesser amount of butter.
If it begins to separate as you are adding in the butter, it’s too hot. Remove it from the burner (which should be as low as possible) and whisk in some more butter off the heat until it comes together again.
Leftover sauce can be kept in the refrigerator for up to one week and used as a flavored butter to saute vegetables!
You can also use red wine to make “beurre rouge” but I ain’t tried it personally.