The four pins
Four pins, three of them wired: GND on the square pad, VCC to one lead of the tilt switch, and SIGNAL on its other lead with a 10 kΩ to GND. NC is connected to nothing. When the left edge of the board is the low one the switch closes and SIGNAL reads HIGH, which is what ACTIVE HIGH on the front says.
Three wires and a spare
The header is four right-angle pins, 2.54 mm apart, printed GND, VCC, NC and SIGNAL from left to right with the parts facing you. GND is on the square pad, and that pad is the only way to tell four identical holes apart. Count from it.
Pick a pin to see where it goes. GND is where the pull-down, the capacitor and the LED end. VCC reaches one lead of the tilt switch and nothing else. SIGNAL is the switch's other lead, with a 10 kΩ and a 100 nF to GND beside it. NC is in no net at all.
What HIGH means here
The front prints ACTIVE HIGH up its right edge. With the switch open the
10 kΩ holds SIGNAL at 0 V: LOW. With it closed, SIGNAL is joined to VCC and
reads HIGH. There is no library and nothing to set up beyond
pinMode(pin, INPUT).
What closes it is the part that needs saying. The brass can lies across the top of the board with its two leads at the left end, and it closes when that end is lower than the other. So HIGH means "the left edge is down", not "tilted": tip the right edge down and it reads LOW, and lying flat it can read either. Which end is lower works through every way up.

VCC is not a free choice
A closed switch puts VCC straight onto SIGNAL, so VCC decides what voltage your board's pin sees. Wire it to the voltage your board's pins run at: 3V3 on an ESP32, an ESP32-S3 or a Pico, 5V on an Uno. VCC is your logic voltage shows what the wrong one does.
When it does not work
The square pad. From the front, parts up and pins pointing down, it is the left-hand pin, and the order is GND, VCC, NC, SIGNAL. The back prints no pin names; turned over, the square pad is on the right and it is still GND.
No. It is soldered to a pad that no trace reaches, so it makes no difference either way. It is there so every TinkerBlock block has the same four-pin header and one cable fits all of them.
The edge the brass can's two leads are at. Look for the two silver wires bent down into the board at one end of the can: that end is the one that has to go down for SIGNAL to read HIGH, however the block is turned.
The brass can, the pull-down, the capacitor and the light, and what each one is for.
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