Thanks for that clarification. After this, I was able to find the International System of Units Wikipedia page which clearly defines a second as per your summary. It's a relief to see that it's a constant formula like that of the Kilogram.
And then there's the candela, still basically defined by how luminous whale blubber is when it is burning:
> Current (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×1014 hertz and that has a radiant intensity in that direction of 1 / 683 watt per steradian.
> Note: both old and new definitions are approximately the luminous intensity of a whale blubber candle burning modestly bright, in the late 19th century called a "candlepower" or a "candle".
https://www.nist.gov/news-events/news/2018/11/historic-vote-...