Requirements I think:

Get Patty's rating up

Eat about 4 hot dogs to get Ben to show up at the street. Visit Ben at the street and agree to help him.

Get the RE where Marvin offers you a black dog and accept it.

Ben will soon notice you dating Patty. On Wk 3 of Dec, Ben will give you a gift to give to Patty. Use it.

Visit the lookout about every other date so that you get all 4 of the lookout REs complete. (eventually you will just go there and leave which means you've done them all)

Keep visiting the Hot dog stand to eventually get a bunch of events where Patty leaves and returns from school. I think you need to take her back to the lookout at this point. This is where you have the option of choosing ducks or baseball. (I chose ducks but I don't think it matters)

Ben will get sick. You just keep going back to the Hot dog stand (Patty's face will be there now) and help her out with everything. After about 3-4 visits, she thanks you and gives you glove wax, spike wax, and Gyroball. You also receive breaking ball points.

I only did this once, but the way it happened seemed as though Gyroball was guaranteed because it wasn't the last thing that you receive during this event. (the waxes were)

I'm not 100% sure if Ben gets sick first and then Patty leaves for school, or the other way around. Either way, if you use this as a basic guideline, you should be well on your way to Gyroball.

All of this is off the top of my head, so I apologize for any slight inaccuracies.