|Pat and Jack Pinnacle
Jack Pinnacle is the taller spire that sits between Pat Pinnacle and the main cliff face. We climbed this route starting from the notch between the two pinnacles. See the approach beta and pitch 1 of Pat Pinnacle for getting to the notch. There is likely a direct route that begins further down on the left side of the spire and ascends the chimney system but I don't know how one would approach it.
From the notch you will want to do a short pitch to reach a smaller ledge on the left side of Jack Pinnacle. Chimney between the two formations and scramble up. The anchor here takes a bomber #4 Camalot in the crack to the right of the chimney, and you can also get some smaller gear behind some questionable flakes.
From the ledge, chimney up through a pod that pinches down into an off-width and forces you out. There is a piton here and some solid cam placements from fingers to hands. The crux (5.9) is the last little bit and you're sure to get a face full of lichen as you struggle up the dirty crack. Above that, you'll be on a nice flat ledge between Jack Pinnacle and the main wall. It's an easy, but somewhat wide, 20ft chimney finishing with a mantle onto the summit (5.4 R/X). There are also new bolts on the east arete of the spire (directly above the Right Side route). But the face climbing up the arete looks hard (probably 5.10+ or harder) and I was unable to reach out and clip the bolts while in the chimney.
Rap from the summit (good bolts) down to the notch. From the notch follow the descent beta for Pat Pinnacle
A light rack to 4" will get you up the final pitch, but you will probably want some bigger cams for the approach pitches.