Not true for the Maronite Church which follows the Latin practice of left to right. Ping!
I’m not sure the direction is that important, but I always use three fingers to represent the Trinity. (There was a big dispute a couple of centuries ago about the number of fingers among the various Orthodox in Russia - all of them a little too tightly wrapped, IMHO!)
I think the American style can be a little sloppy. Latin Americans and many Europeans tend to cross themselves with one or three fingers and kiss their fingers afterwards. I often make a tiny sign of the cross with my thumb on my chest when a regular one would be impossible or ostentatious.
That said, I don’t think it’s that important. But it should be careful and respectful, unless you’re at the point of death...in which case, cross your arms.
The Biblical Roots of the Sign of the Cross
St. Francis de Sales: How to make the Sign of the Cross [Ecumenical]
The Sign of the Cross [Catholic and Orthodox Caucus]
The Sign Of The Cross [Catholic Caucus]
Sign of the Cross, Sign of All Time (User's Guide to Sunday)
Cross, Sign Of
The Sign of the Cross
In the Name of the Father . . .[The Sign of the Cross]
The Sign of the Cross
The sign of the cross capable of killing microbes