If read-counter is already incremented once a millisecond, use that to time your LED flashes:

void wait_function() {
  timer_init();
  bool LED_State = LOW
  while(read_counter()<30000) { //30 second wait
    // A LED blinking at 1 second intervals ???
    if (read_counter % 1000 == 0) {
       LED_State = !LED_State;
       digitalWrite(LEDPin, LED_State ? HIGH : LOW);
    }
  }
}

That code will turn the LED on for one second, then off for one second, etc. (For a total cycle time of 2 seconds.) If you want the full on-off cycle to last 1 second, lower the if statement's value from 1000 to 500.

If read-counter is already incremented once a millisecond, use that to time your LED flashes:

void wait_function() {
  timer_init();
  bool LED_State = LOW
  while(read_counter()<30000) { //30 second wait
    // A LED blinking at 1 second intervals ???
    if (read_counter % 1000 == 0) { //Switch 1000 to 500 here if it flashes too slowly
       LED_State = !LED_State;
       digitalWrite(LEDPin, LED_State ? HIGH : LOW);
    }
  }
}

That code will turn the LED on for one second, then off for one second, etc. (For a total cycle time of 2 seconds.) If you want the full on-off cycle to last 1 second, lower the if statement's value from 1000 to 500.