I don't know whether your tractor had the third brake or not.
The '38 ZTU I have didn't have one when I got it in 1993. My cousin has a '40 ZTS that has the pedal. I always wondered if the pedal would work with the pto power lift mounted on the tractor or if there would be a clearance problem.
It could have been removed for some reason in the last 70 years or so.