1) Hate to say it, but maybe you have become a Begonia Bug....take a look at
for an example of someone who is (maybe by now was
...) a Begonia Bug. The story involves Begonia Rex Cultorum, perhaps (and I emphasize PERHAPS) also referred to as Red Knight but also Scarlet Knight....
Which started out with red leaves which then became white and then became scabrous and purple....
Begonias have their own ideas, being tropical plants that Canadians/Americans try to grow in non-tropical conditions. Begonias react unpredictably--VERY unpredictably, according to this story--in the conditions we can provide in North America, even when their faithful minions cater to their every whim.
2) The Internet is, despite what many believe, *not* the be-all and end-all of plant identification. The situation with which this thread began--cobalt appearances in the leaves--is a perfect example of what camera + Internet can produce. It stymied identification for quite some while, since there seem to be no begonias anywhere in the world with the cobalt coloration which was plain in the original photos. Also, color registration differs from one brand of monitor to another *and* from one combination of operating system + monitor to another.
3) Although The Helpful Gardener forum is liberally festooned, so to speak, with experienced gardeners of almost every possible description, from bonsai enthusiasts to market gardeners to rose fanciers, I don't think anyone on the forum is a professional botanist. Thus we're all amateurs when it comes to plant identification, dependent on other amateurs for our information. And, sometimes, this does mean that an absolute, 100% definitive ID is not possible based on available information.
4) Search criteria: I used Google for this particular search, and the key words "Red Knight Begonia photo." The first hit had four distinct photos of the plant, no two of which were alike. In fact, two had red leaves, one was in a mixed arrangement, and one had white leaves. (Just like the above story experienced.) There were many other photos as well. Try another search using the criteria/key words I used; maybe you'll find photos that are more helpful to you.
5) My response should not be taken as a shutdown of this pursuit or a close-out of this discussion; on the contrary, it is meant as a spur to your *own* continued research and that of other interested parties. Ideas:
--Look around San B'do County for in-person garden clubs with begonia interest groups.
--Tropical plant nurseries will have knowledgeable staff.
--The UC and Cal State systems have Botany, Horticulture, and related departments with students and faculty who may be pursuing studies involving begonias.
*These* will be the people who can look at your plant in person and help you identify it and prepare for whatever it will need in the future: special growing conditions, how to propagate, how to achieve maximum growth; whatever you're looking for this plant to do for you, far beyond the ability of anyone who has tried to help in this thread.
A little knowledge is a dangerous thing. It's like a small itch: it leads to MORE. MORE questions. MORE knowledge. Which generates MORE questions, but on a new, more complex level.
It never ends.