1957 Ford park will not hold

['46Ford]

I have a 1957 Ford Ford-O-Matic 2 speed. When it is in the park position the car still rolls, does not lock up. All the other gears, reverse, neutral, drive work fine and are aligned with the shifter marks. I have checked the linkage and it is tight, no loose bushing, and the lever cannot go any further in the park position, I was thinking it may not be fully engaging but that does not seem to be the case.
Is there an easy fix to this. One good thing, my emergency brake does work good.