As a PMM, I tend to view the RACI as PMM being responsible/accountable and CS being considered and PM being informed/potentially considered.
But it depends on your org and how you're structured. The reason I say PMM is because I think the value of an advisory board is to help understand new trends, forecast the future, and help guide the product. So its about the intersection of the product and the market.
CS teams could also lead and advisory board as well. I think the best solution on who should lead the creation of the advisory board being whichever team has the bandwith and available time for the critical thinking to maximize the program. Better to have the "wrong" team lead it if they are giving it real thought than having the "right" team lead it and go through the motions without maximizing its impact.