---

unsigned long timer = 0;
void setup() {
  pinMode(2, INPUT_PULLUP);
  pinMode(13, OUTPUT);
}
void loop() {
  if(digitalRead(2) == LOW) {
    digitalWrite(13, HIGH);
    timer = millis();
  }
  if(millis() - timer > 10000) { // 10 секунд
    digitalWrite(13, LOW);
  }
}