OK, bear with me. Im not a good writer at the best of times (otherwise Id have a proper job) and Im slightly pissed. Ill waffle with some background and then get to the specifics of your case.

Air is pretty transparent, so visible rays, shafts and beams are produced by light interacting with suspended particles (dust and tiny water droplets mostly henceforth referred to as stuff). Refraction, reflection and diffraction (of light by stuff) all play a part in the formation of visible rays. Instead of all the light racing off in one direction as it usually does (such as in a vacuum), some gets bounced and bent when it interacts with stuff. If, from the point of view of an observer, the bounced and bent light reaching the eye is brighter than the background a ray of light is seen.

There is much more stuff in the lower atmosphere to cause bouncing and bending than in the upper atmosphere thats why a clear blue sky is always brighter around the horizon than overhead. Except immediately around the position of the sun backlit stuff is the most visible of all.

When the sky is free of cloud, a low sun will illuminate the lower atmosphere stuff around it evenly, and all the bouncing and bending effects will be fairly uniform and not particularly noticeable. But if broken cloud intervenes between sun and observer, only some of the lower atmosphere stuff will be directly illuminated (the rest is in shadow) and that directly illuminated stuff will do its bouncing and bending thing.

If the bounced and bent light reaching the eye is brighter than the background, be it a dark hill, reverse side of cloud, or upper atmosphere, then a visible ray, beam or shaft will be seen.

Does that make sense? I think so, but then Ive had beer plus some Bruichladdich 10 (which I could only gain access to by removing the poxy Sainsburys security device, that some uninformed tilly left on my purchase, with a soldering iron).

All it takes is for the bent and bounced light (after interacting with stuff) to be brighter than the background. If the background upper atmosphere is dimmererer than a lit column of lower atmosphere stuff, then the latter will be visible as a ray/shaft/beam.