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.

On these boards there is one more step between BL and the lamp: BL does not go to the controller at all. It goes to the gate of a transistor, and the transistor decides whether the lamp's current flows. A 10 kΩ resistor holds that gate at the level that keeps the transistor off, so the lamp is dark until BL is driven, and also while BL floats.

Pick a board and leave BL alone: the lamp is off. Drive it from the library: the lamp follows backlight(n). That is the same on all six. What differs is which level means on, and it differs because of which transistor is fitted.

Five boards: the transistor is below the lamp

The 1.8, 2.0, 2.4, 2.8 and 3.5 inch boards have a BSS138, an N-channel transistor, between the lamp and ground. The lamp's other end is on 3V3 and a 2.2 Ω resistor is in its current path. BL is the gate, and the 10 kΩ goes from the gate to GND. BL high turns the transistor on and lights the lamp. BL low, or nothing, leaves it off.

The 0.96 inch: the transistor is above the lamp

The 0.96 inch has an AO3401, a P-channel transistor, between 3V3 and the lamp. The 10 kΩ goes from the gate to 3V3, which holds it off. BL has to go low to turn it on. So on this one board, 255 on the pin is dark and 0 is bright, and nothing about that looks like a fault: the screen still dims and still brightens, only the wrong way round.

The library already knows

backlight(0) to backlight(255) is brightness on every board, in both languages. The polarity is a column in the panel table, so the constant that selects the board selects the polarity with it, and there is nothing to remember. The library drives BL with 5 kHz PWM on every board, so full brightness is 255 rather than a different call.

The figure is for the 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.

The jumper, and the pad you must then leave alone

The BL solder jumper ties the pad to the level that lights the lamp: 3V3 on the five boards, GND on the 0.96 inch. It ships open. Bridged, the lamp is on at full and BL is a fixed level.

That is a fine way to save a pin. It is also the one place the board can be hurt from the sketch: the library drives BL, and a driven pin against a strapped rail is a short through the pin. Step the figure to bridged and drive it from the library below full brightness to see it. The cure is one line, pins.backlight = -1, set through setWiring() before begin().

What the lamp costs

It is usually the largest single load on a board like this and it switches on all at once. On a host 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.

begin() switches the lamp on at full, so the step happens there and cannot be softened from the sketch. A supply with headroom is the cure.