My favorite approach to Pallet Mtn is from the east. I start at the west Mt. Williamson Trailhead ("A"), head up to the "crest" of the PCT ("B"), and then summit the named summit of Mt. Williamson ("C"). From the named summit, I proceed to the true summit ("D"). Oddly, the register can is usually on the summit between the true summit and the named summit.
From the true summit, I proceed NW to the unnamed summit at "E", then to "F" (Pallet Mtn) and Burkhart Saddle ("G"). There's potentially water at "H" and "I." I then hop on the ridge starting at point "J" and summit Goodykoontz ("K"). From Goodykoontz, I ascend the various knobs back up to the unnamed peak at "E" and then retrace my steps back to my car.
Alternatively, one could descend from Goodykoontz via its SE ridge to one of the forks of Little Rock Creek, cross the creekbed, and then ascend back to one's car. Very doable albeit steep, but I think you might be violating the "Frog Zone".
HJ