Is there a way to have the LED switch on after 10 readings or say a minute?
You want to light the LED, when the same chip was read 12 consecutive times. So I would suggest something like this:

Inside your void loop() function you use the millis() coding style (refer to the BlinkWithoutDelay example, that comes with the Arduino IDE) to scan every 10s for a chip. Then you add a counter variable to count, how often the same chip was scanned. If this counter variable is >=12, you turn on the LED. If a different chip was scanned, you set the counter to 1 (since this chip was now scanned 1 time). This leads to a code something like this:

#define READ_INTERVAL 10000
int read_counter = 0;
unsigned long read_timestamp=0;
String last_identifier="";
void loop(){
    if(millis()-read_timestamp&gt;READ_INTERVAL){
        // Read the chip
        if(card_identifier == last_identifier)
            read_counter++;
        else
            read_counter = 1;
        if(read_counter&gt;=12){
            digitalWrite(LED_PIN, HIGH);
        }
    }
}


Be sure to use unsigned long with the millis() function, to prevent it from overflowing to a negative value.