I just replaced the wiper motor on my 68 (it had never worked since I obtained the car)
I have tightened the 3 mounting screws to the firewall but noticed that when turned on the wiper motor itself is moving in reaction to the movement of the wiper arms. The 3 mounting screws are fairly tight (did not want to over-tighten them).

Is the motor itself supposed to move when the wipers are on and moving ?

Thanks,
John

No, it should not move. Perhaps the linkage is incorrect.

There are three rubber grommets that fit into the housing. It's possible that they are rock hard or are missing some surface area on them not letting you pull it tight to the firewall.