Notice that the maneuvers are essentially the same as knits and purls. Stitches are cast-on in knit-purl (or purl-knit) pairs, which is why this cast-on does not work well for plain stockinette.
To cast-on a knit stitch:
duck the right needle front to back underneath the front yarn,
wrap the back yarn as you would when making a knit stitch Continental style,
bring the yarn forward as if pulling up a knit stitch.
To cast-on a purl stitch:
duck the right needle back to front underneath the back yarn,
wrap the front yarn as you would when making a purl stitch,
take the yarn backward as if pulling up a purl stitch.
If you can remember these two maneuvers, you should be able to remember how to work Italian cast-on whenever you need it, without having to look it up every time.