Tire rotation was needed with bias ply tires back in the day.
today's radial tires not so much. Still a good idea but not needed near as much as some think.
seems to me the frequency of rotation in the owners manual/service booklet is high.
The purpose of rotation is to get the drive wheels on the back and the wear equalized on the steering contact patches, etc.
So you can either do it as stated in the owners manual or you can inspect and do it as needed. All you want is even wear and for the tire to be nice and square, not rounded off on any one more so than the others.
I'm rotating at every second oil change, it was just too frequent for me at every one...mind with the kms I put on my oil changes happen every 3-4 months.
If you don't have directional tires you pull the fronts to the back, leaving them on the side they started on and bring the rears to the front, switching them over, side to side. So, its not really an X. That is the recommended way for FWD. Which the Patriot is for most of its driving time. . Important thing is to remain constant. Don't fwd cross one time, rear cross the next and cross both axles the next.
If you have directional tires you go front to back and back to front keeping the tires on the same side of the vehicle for the life of the tire.
To my mind its better to rotate up on a lift, you get to inspect and shake stuff that you can't when doing it on the driveway.