Can potentiometers are typically about 1 cm high with a visible screwdriver slot in the top. Tuning capacitors typically have a screwdriver slot and a visible wedge shaped blade under the plastic cover.
Can tuning coils are typically 1-2" tall square cans with a hole and something down in there not necessarily near the top. Sometimes the slot is flat screwdriver, sometimes the slot is hex allen screw.
Your 12 cans are probably tuning inductors, They are a coil with a sintered iron slug in them to screw up and down and change the inductance. As sintered means made of powdered metal, the slugs are a bit fragile, and act differently with a steel tool touching them than if you touch them with brass or plastic. The slugs are also likely to be rusted and stuck.
Divider organs before top octave generator IC's (about 1974) have 12 oscillators and 12 tuning devices, and divide the top octave by 2 for each octave below the top one.
I would check the power supplies to see if they are nominal before I went buying tuning tools and risking breaking slugs if you have coils. Things don't work properly if the power supplies are way off, and the electrolytic caps in the power supplies are pretty well guarenteed to have decreased in value due to leakage of the water inside past the 20 or more year old rubber seal. These caps have a plus on one end, or after 1980 minus's in balls on a stripe, pointing at one lead. They are measured in microfarads, mf before 1980 and uf afterwards.
For a tuning reference, if your ear is not perfect, toy keyboards from the charity resale shop are portable. I use my H100 organ to tune my piano, but at 350 lb it is certainly not portable.