const uint8_t pinRele = 13;
const uint8_t pinBtn = 7;

uint32_t ritardo = 10000;
uint32_t onTime = 0;

int32_t releON(const uint8_t pin) {  
  digitalWrite(pin, HIGH);
  return millis();  
}

void setup() {
  pinMode(pinRele, OUTPUT);
  pinMode(pinBtn, INPUT);
}

void loop() {
  if (digitalRead(pinBtn)) {
    delay(100);   // semplicissimo debounce del pulsante
    // if (digitalRead(pinRele) == LOW)  // Partenza del conteggio dal fronte di salita del PIR
      onTime = releON(pinRele);
  }

  if (millis() - onTime >= ritardo) {
    digitalWrite(pinRele, LOW);
  }
}