The backlight runs both ways

Two circuits, one board

The picture and the light are not the same thing. The controller draws into the glass whether or not there is a lamp behind it, and the lamp shines whether or not anything has been drawn.

That is why a dark panel is ambiguous and why it is worth resolving the ambiguity first: tilt the screen towards a bright lamp and look at it at an angle. If the picture is there in the reflection, everything except BL is working.

And on one panel, the switch is upside down

Pick the 0.96 inch and switch to driving the pin yourself. Now the slider runs backwards: 255 is dark, 0 is bright, and every value in between is the wrong way round.

Nothing about that presents as a fault. The screen still dims. The screen still brightens. The scale simply runs the other way, so a sketch that fades the display up fades it down instead, and a sketch that turns the backlight "on" at boot turns it off.

Of the six panels in the kit, only the 0.96 inch is wired this way.

The library already knows

backlight(0) to backlight(255) is brightness on every panel, in both languages. The polarity is a column in the panel table, so the constant that selects the panel selects the polarity with it, and there is nothing to remember.

It always uses PWM, too, on every panel — so full brightness is simply 255 rather than a different call, and dimming works everywhere rather than on the panels somebody happened to test.

The figure above is for the two cases where you meet the polarity anyway: reading somebody else's driver, or writing your own. If you ever need to override it:

display.setBacklightActiveLow(false);   // any time, before or after begin()

printInfo() reports the polarity and marks it (forced) when you have overridden the table, which is how you tell a deliberate override from a misconfiguration three weeks later.

What the lamp costs

It is the largest single load on any of these panels and it switches on all at once. On a board whose 3.3 V regulator is already close to its limit, that step can drop the rail far enough to reset the microcontroller — which looks like a crash in the sketch and is not one.

Bringing the display up with the backlight at zero and raising it over a few tens of milliseconds avoids the step entirely, and it looks better anyway.