Ok, I don't see why any designer would want to include the possibility of LCD flip where such a possibility would never be desirable.
As seen on e.g. cellphones, it can be very useful, though. That, too, can be implemented in various different ways, but the ones I have, can mirror horizontally and/or vertically with just one simple command at any time, without any changes to the image data itself.
I did realize there is one major difference between the controllers I've used and considered/listed here, and the HannStar one at hand: mine are all programmable (with SPI, I2C, MIPI, other serial, or a parallel connection for commands, often using the RGB pins for commands), whereas the HannStar one is controlled via pins only; no command interface at all. Perhaps that explains it?
They would surely just wire this out and use the INIT stage to set it as required.
These controllers are surprisingly complex devices for their size: the dimensions in the datasheets are given in micrometers, with bumps on the order of 40µm = 0.04mm in size. I know
nothing about their internal implementation, so I just don't know.
Look, this is pretty much a moot point.
The problem here is clearly to do with dirty ribbon cables, reseating them is the solution.
Problem solved.
Yep. If reseating doesn't help, examining the resistance between pin 35 and 36 on both the FFC and the connector will show if there is a weak short, like a tin whisker (which can happen with leadfree solder), and careful inspection and possibly scraping/brushing, then reseating, should help.
Whether it is moot or not, it is good to be suspicious/critical, and question things –– definitely so about what I post.

I do feel very stupid for how I tried to express the idea that when one finds a solution, retracing ones steps back to where one started and if possible posting a note about the solution is useful; the same –
path compression – is used in many optimization techniques, and makes a critical difference for e.g.
disjoint-set data structure operations. (It's a data structure that lets you say which pairs of elements are connected, and it tells you, at any point, which of the connected sets thus formed each element belongs to. When using path compression, it is extremely efficient, but without path compression it is slow as molasses.)
It came out all wrong. Apologies about that.
