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The VT01 famiclone can drive an STN-type LCD. According to the VT01 datasheet, the six bit color numbers have a different meaning in that case: rather than specify luma&saturation +phase, they specify four levels of red (bits 4 and 5), four levels of cyan (bits 2 and 3), and .... fours levels of something that the datasheet does not explain at all. The description of the STN-relevant chip pins is too cryptic to be intelligible.

A small number of ROMs exist that use color numbers formatted according to that specification. They are named "Portable FC-LCD 14-in-1 Game (Ch) [!]", "Portable FC-LCD 14-in-1 Study (Ch) [!]", "Portable FC-LCD S1 (SB01) Eng-Chi Dictionary 1 (Ch) [!]" and "Portable FC-LCD S2 Eng-Chi Dictionary 2 (Ch) [!]". I can make a palette that sort-of gets red and cyan right (first: normal NES palette, second: STN LCD palette):


But the two extra bits are definitely used for something (first: Eng-Chi Dictionary screen using just the Red and Cyan bits, second: same screen using just the two unknown bits)
At least in the last image, these extra bits would either serve as a highlight or a shadow.

Now, I could just assume as these bits are for some sort of extra brightness, or "intensity", and make up some formula to use them based on what looks nice, but maybe somebody who has some experience with these types of displays has an idea. Unfortunately, I could not find a video or image showing how these particular displays look exactly; all videos I could find are of devices having TFT or similar displays that just show the normal 2C02 colors.

Reading the datasheet, there's only 4 wires carrying the segment data from the VT01 die to the LCD.

Since they specifically call the signals "segments", that implies to me that the LCD interface actually modulates its output on subsequent vertical refreshes, effectively PWMing the segment opacities, rather than the LCD segment drivers themselves driving the segments to intermediate voltages.

It calls out a choice of STN Red/Cyan with "120x2x240" or STN BW with "240x240". Implying to me a fixed pixel clock, and that the same segment signals are either divided among color or just monochrome.

My best guess is that the two LSBs are actually unused. ... and that the display will have a gamma of 1, not the standard PC 2.2

(That said, the hanzi in the dictionary don't look very good without those extra bits...)

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The game "Dragon" in the 14-in-1 games cart does imply the two extra bits are shadow, as after each level is completed the game fades to $3F before going to solid $00.... although that could just be a vestigial bit from the original 2C02 palette, because it also fades down the $30s bits and then from any color $0x to $3F when becoming darker.

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edit #large: STN screens also have a typical contrast ratio of about 10; you're certainly not going to get nice blacks out of these screens.

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Comparing the original Soccer (JU) to the "World Cup" entry in the games cart, only two entries have those LSbits set in their palettes:
and those entries are ones where those two colors would be same and are adjacent in the relevant sprite. Maybe it causes some very subtle difference in color?

Maybe it just sets the PWM phase? A 4-level PWM just requires three phases: ABB where BB is the MSbit and A is the LSbit; maybe things look different enough to be visually distinct by changing the phase?

"Goblet Tower" on the "Portable FC-LCD 14-in-1 Study" cartridge has colors that only have the extra bits set.

"Goblet Tower", like "Dragon", also only remembers to fade out the $30s bits when it fades in and out, so I fear it's another incomplete palette hack. The details in color $03 is a set of palm trees in the background, and the shadowed edge of the front bezel.

addressing some questions you deleted:

STN speed is pretty slow. I'd expect speed comparable to the gameboy pocket (MGB) (but faster than the original DMG) (example video, you'll want to mute it)—it looks to me like a reasonable emulation is "video = (newframe+oldframepreviousVideo)/2" —if you're working with gamma=1 i.e. it's an IIR filter not an FIR one

Redraw frequency for the panel is almost certainly the same 50 or 60 Hz that the VT01 is generating video at.

I was assuming the "phase change" bit would change the pattern from ABB to BBA, not invert things. In hindsight, that wouldn't do anything visible on colors $00/$30/$0C/$3C...

STN contrast ratio is terrible. I'd expect an accurate emulation to involve a palette with reference values closer to (assuming monitor gamma of 2.2) (59,110,142,167) than (0,85,170,255).

VBA has some LCD emulation. None of them look particularly authentic, but I'd say they're closer than none at all.

Eh, the DMG's transition speed is barely slower than the MGB's. The DMG is far better than the shitty STN screens in cheap early '90s laptops.

Does anyone own one of these odd famiclone units and can shed some light on how it appears?

Page 12 of the original Game Boy's manual says it uses an "STN type dot matrix LCD".

STN (and its descendants) are more-or-less the only option for low power high-pixel-count displays before active-matrix displays hit mass market. (TN doesn't support high enough multiplexing to be an affordable option)

STN technology improved between 1988 and 1996. Per mikejmoffitt, apparently mostly in terms of contrast (or perhaps instead max brightness), and less in terms of response time.

The panel of the Game Boy Pocket MGB has better contrast than the STN (Super-twist neumatic) panel of the original DMG Game Boy. However, MGB also has much more prominent vertical streaking than the DMG. It is as if they traded contrast ratio for row/column access time. The contrast of the DMG can be hugely improved by a bivert mod, the battery life is longer, the controls are larger and the audio output is far better than the poorly filtered pocket.

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Nerdly Pleasures - My Vintage Video Game & Computing Blog

[pedant] Nematic, from greek "nema", "thread" (cognate: nematode). Not pneumatic from greek "pneuma", "wind" [/pedant]

Thanks everyone for your input. I think I will implement this as ignoring bits 0 and 1 for now, as those bits being used really does seem like the result of incomplete palette hacks, until real hardware indicates otherwise. I am going to apply some gamma correction as well, though maybe not as extreme as an exponent of 1.0/2.2 and a value range of 59-167. Such accuracy would require measuring the exact colorimetric values of the STN's red and green phosphors (if that is what they're called), otherwise it would be a fake kind of accuracy.

I would expect brightness and contrast comparable to other STN displays; people have extensively measured the contrast ratio of the MGB and DMG.

Pretty certain all the contemporary consoles were also STN or FSTN (Lynx, Game Gear, TurboExpress); TFT technology hadn't hit mass-market yet.

That said, it does indirectly raise the question: we can't know whether these had a backlight.

A 10:1 contrast ratio would be 90-255 on a gamma 2.2 screen. Whether one thinks it should go as bright as 255 is a valid question.

(edit) Emutalk thread 1: BlackZero's calibrated palettes have the DMG at a maximum brightness roughly 20% reflectance maximum and a contrast ratio of only about 5:1, and (emutalk thread 2) the MGB at 32% reflectance maximum and a contrast ratio of only about 3:1. ... I don't think I believe that latter bit. His contrast ratio for the green EL backlit Gameboy Light is about 6:1.

(edit2) The other really big thing about the appearance of these screens per the datasheet is that there are no subpixels, it's actually a checkerboard; this would have a significant effect on the appearance. Whether one wants to emulate that is a good question.