When I started photography every roll of film had an info sheet that included a discussion of what the sunny f-16 meant. That ended in the 70's sometimes, although it may have been later. I took my first university photography class in 1968, using medium format with a hand held meter.
In Washington D.C at high noon on the fourth of July the "sunny f16 rule" becomes the sunny f/22 rule, it is that bright.
"Full Sun" f/16 (sunny- as bright as it can be, high noon give or take two hours)
Hazy bright - one stop open- f/11 (clear shadows with a sharp line. Also beyond the +/- two hour window)
Cloudy bright - two stops open - f /8 (distinct shadows, but soft edges)
Cloudy - three stops open - f/5.6 (no shadows, but still more than 2 hours after sunrise or before sunset.
Overcast - four stops open - f/4 (bleak and dreary, bad weather imminent),
The time of day affects the sunny f/16 rule, when used by an experienced and knowledgeable photographer. That is built into the "rule". Such a photographer knows that mid morning and mid afternoon are one stop open from full.
When I was in military photography school and we slept in the barracks someone might ask what the weather was like. If the answer came back "F/8 at 11:00" , we knew what kind of day it was. Cloudy bright.
In truth, if you know virtually nothing about photography (light-writing), the sunny 16 rule fails miserably, consistently.
If you understand why your images were/are under-exposed, over-exposed, or spot on, and what you should gave done to correct the problem, the Sunny 16 rule works always and consistently - at it's intended purpose.
It is meant to give well exposed, amateur grade, scenic photos. In use by an experienced photographer, it works rain, snow or shine, not to produce sellable images, of salon quality, but to record a scene worthy of any family album.
The full application goes well beyond simply "Sunny and f-16".
If it is hazy bright three hours before high noon, I need to open one stop for time of day, one for hazy bright. The "sunny 16 rule" says my exposure is f/8. If it is winter, with the sun low in sky, I know to open another stop.
If my subject is in full shade, (overcast) I know to open four stops. The sunny f16 rule says f/2 - or f/1.4 in the winter (four stops open from f/8 or 5.6).