So you suspect that the worm is not engaging properly with the worm gear?
Did you verify that the universal coupling is not the problem?
I found the exploded diagram from which I snipped the above picture right on Kato USA website.
On thebu main page, under the N scale button on the top I selected N Scale North American Locomotives.
Then clicked on FEF3, then Maintenence, then on
Downloadable (3MB) Exploded view diagram for the N scale FEF-3You can get the part # if you go to the Kato's parts shop (link on the bottom of the main page) then in the parts store just search for FEF. That will bring the parts listings including the part you are looking for.
The other question I have is how did the problem develop? Did it just happen suddenly with no changes made to the model, or was some sort of work done on the mechanism prior to then the problem showed up? Or was the loco dropped or some similar thing happened?