Do you have any more particulars in regard to the execution – such as an approximate date? Where did you get the info about ‘near a large rock’?

I live near Santa Fe and could poke around the cemetery for the heck of it.

According to the website you provided:
“After a time, he returned to Missouri and was discovered. The amnesty papers in his pocket did him no good. He and a man named Farley were shot. The people of Santa Fe, Mo., would not allow them to be buried in the cemetery so they dug one grave outside the fence, putting both Jackson and Farley in the single grave.”