According to what I have read, autosomal barring is not caused by a different gene, just a slightly different combination of the same genes that are involved in the other pencilling, double lacing, barring, and also spangling.
https://sellers.kippenjungle.nl/page2.html
About 2/3 of the way down this page, there is a chart showing quite a few different patterns and which genes combine to make them. Everything in the chart has the pattern gene, but when you change the e-locus or have various combinations of Melanotic, Dark Brown, and/or Columbian, plus hen feathering for Sebrights, you get quite a few different results.