I believe the Dan Jackson you are referencing (the rug pattern) is a different Dan Jackson than the one who made your piece. The Dan Jackson who made the rug pattern jewelry uses this mark.
The “Jackson” hallmark you showed a picture of, made jewelry in this specific style:
Who knows? Both types of jewelry are in the style of overlay. And Jackson is a common last name. They could very well be the same artist. I hope someone more knowledgeable than I can confirm. Artists change their hallmarks over time.