Not that I'm any authority , but I don't recall seeing one like that in any of the literature I've seen on Simplex .
This what the Seller wrote in that auction :
"Original headlight servi cycle made by s&m lamp co Los Angeles very hard to find the original light original lens ballast etc.... 6" across this is the one your looking not a repro this is the original late 1940's in great shape will clean up !!! Good luck !!!"
I've never read anything about a ballast being used by Simplex , either .
Pete .