The pull-down and the light

A switch needs something on the other side

A switch on its own gives your pin two states: joined to VCC, or joined to nothing. Joined to nothing, a pin floats, picks up whatever is nearby, and reads HIGH or LOW at random. The 10 kΩ from SIGNAL to GND is there so that "nothing" means 0 V. That is a pull-down, and it is why this board is active high: the resistor holds LOW, and the switch overrules it with VCC.

Close the switch and follow the dashes. Current comes in at VCC, through the balls, and splits: 0.33 mA down the 10 kΩ at 3.3 V, and about 1.3 mA down the 1 kΩ and the LED. None of it comes from your pin, which only reads the voltage. Bailin's sheet puts the closed switch under 10 Ω, so it drops at most about 16 mV of it.

The capacitor

C2, 100 nF, sits from SIGNAL to GND beside the 10 kΩ. When the balls close the switch it charges through them in about a microsecond, and after that nothing flows into it. When they lift off, it keeps SIGNAL up while the 10 kΩ and the LED drain it: about half a millisecond before an Uno reads LOW, about a millisecond on a 3.3 V board. So a ball that loses contact for less than that never shows. A rattle is not a tilt draws it.

The light shows the switch

The LED is on SIGNAL, fed through the switch, so it lights when the balls are on the contacts and not otherwise. It does not need a sketch, or even a microcontroller: VCC and GND alone are enough to see it work. When something is wrong, that splits the fault in two, which when it reads wrong uses.

INPUT, not INPUT_PULLUP

The pull-down is already on the board, so the pin needs no resistor of its own: pinMode(pin, INPUT). INPUT_PULLUP adds the chip's internal pull-up, which pulls the other way against the 10 kΩ while the switch is open. On an ESP32 that lifts the open level to about 0.6 V. On an Uno, with the pull-up at the strong end of its 20 to 50 kΩ range, it reaches about 1.7 V, more than the 1.5 V the pin promises to read as LOW.