Me personally? I'd just ride and ride and ride. As often as possible.
I'd walk the pattern some here and there, but not drill it hard.
Get to know each other, get him to be a solid mount, and confident in you. Then worry about running patterns.
A Good barrel horse can get down when it's time, then walk off like its just another day in the park.
A smoking fast, needs lead or pushed in barrel horse, IMO, is useless.
Don't set your focus on barrels but more so on a GOOD horse, and I bet you'll do just fine.
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