I donít think that sudden failure precludes the motor as the source of trouble. If the motor is of the graphite brush/commutator variety, the brushes might have worn to the point of loosing electrical contact with the commutator.
If thatís the case, simply replacing the brushes and cleaning any graphite deposits from the commutatoróespecially the gaps between the conductive segments might restore operation.
If the motor needs replacing, then you should be able to find one of the correct size and specifications. Simmon Brothers or Berkey Marketing Companies, whichever was the owner at the time of your enlargerís manufacture, almost certainly didnít make electric motors, but bought them from a vendor just as it did for almost all of the inner components.
The focusing control is likely easily analyzed and understood by someone with experience with electrical devices. Iíd expect that the heart of a fine focusing control as youíve described it was some sort of variable resistor to slow the motor so as to ďcreepĒ the focus slowly without overshooting.
That or a reduction drive might have been used. I havenít specific knowledge of the system used for the electrically-driven fine focus so Iím necessarily speculating on how the fine focus is driven on this machine.
Enlisting the aid of a competent electrical or electronics technician might make the source and particular cause of the fault readily apparent. At least in that way you wouldnít be aimlessly speculating as to the cause of the problem.
In most cases, when such devices are opened and investigated it turns out that all the components are off-the-shelf industrial products that in most cases can still be obtained provided one knows where to look.
Usually, the only proprietary parts (custom fabricated for one particular product) are circuit boards and sometimes integrated circuits (but a custom IC isnít likely for a simple motor controller).
Post #2 makes a good point. Make sure that there isnít gummed lubricant on the rails as that could turn any lubricant into varnish after 40 years or more. Dried lubricant might be inside some part of the unit causing the problem. You wonít know until you investigate.
This might take some research and possibly assistance from someone knowledgeable in electrical matters.
It almost certainly can be made to work again.