Does he appear in Free Roam, course i've never seen him there? Same with that Vern Timmons.
I checked from Free Roam, and founded out that this Nash Stringer isn't this guy, this guy with moustache is Vern Timmons and the other one is Nash Stringer. Go to LAN in Multiplayer, get bounty over 500 $ not 1000 course then the marshals will come, then go to Riley's Charge, and wait there a while. I suggest to start from Armadillo and then lose your wanted level, then go to Riley's Charge. That's how I have checked out all the Sheriff names like Waylon Myles and Buford Ackley, after Hobbes found them. PS: If you fail to found those Nash and Vern, exit LAN and then return to LAN.