How to find the nodal point of a lens?

[Paul Fitzgerald]

How did the old Cirkut pano cameras work? They did not rotate around either nodal point.

[Emmanuel BIGLER]

It is simply adequate to rotate around the lens aperture

Yes, exactly, but not around the physical location of the aperture, but instead around the location of its image as given by the first half of the lens, looking from the front side of the lens. In some lenses like the apo ronar, the distance between the iris and the pupils is very small, about 1% of the focal length.
"The image of the iris seen from front" is simply the definition of the entrance pupil and this is the right place to rotate the whole assembly (lens + camera + detector). for panoramic stitching afterwards.

How did the old Cirkut pano cameras work? They did not rotate around either nodal point.

I do not know the details of the Cirkut camera, but if its principles are similar to what I know in other panoramic cameras like Noblex or Seitz panorama cameras where the lens moves with respect to a fixed film holder, hence the rotating point of the lens should in principe be the rear or exit nodal point of the lens usually named N' = H'.
If the Cirkut works differently, i'd be interested to know how the Cirkut works.

The two problems are different.
In panoramic stitching you want to avoid unwanted parallax effects that could be detrimental to the stitching process. So the condition you are looking for is that objects that look aligned on image #1 are still aligned on image #2 after rotating the whole camera for shot#2. The proper place for this is the entrance pupil.

In panoramic cameras where the lens rotates with respect to a fixed film, film being fixed with respect to the landscape, you need to avoid image blur during the lens movement. Only a thin strip of the image is exposed at a time, a slit moves just in front of the film in synchronism with the lens.
For far-distant objects, the rotating point minimizing blur when a lens rotates is the exit nodal point N' or H'.
This is valid only for far-distant objects, see the attached pdf diagram for the explanation.

For example, a very special (hypothetical ?) panoramic camera operating at the 1:1 ratio with a symmetric lens should probably rotate the lens around its center of symmetry to minimize image blur during the rotation process.

Note that the Alpa Rotocamera (was actuallly made by Seitz AG, not by Pignons SA) has a special operating mode ; the whole camera rotates, i.e. the lens is fixed with respect to the camera body, but the film moves in the proper direction and at the proper speed so that the film is fixed with respect to the landscape during the movement. This is in fact equivalent to the Noblex system, but for an observer attached to the film ;-)
In this case, the rotation point should also be the rear nodal point of the lens.
Actually in the Alpa Rotocamera which I have examined a few times in a friend's collection,, the lens is a 75mm -6.8 Grandagon-N, which is almost symmetrical, hence the pupils are located at the nodal points, and are very close to each other. So it is not easy without a precise measurement tool to know exactly where the engineers have decided to rotate