You could flash the lights:
void setup()
{
pinMode(Player1ButtonPin, INPUT_PULLUP);
pinMode(Player1RelayPin, OUTPUT);
pinMode(Player2ButtonPin, INPUT_PULLUP);
pinMode(Player2RelayPin, OUTPUT);
// Signal for attention. Blink both lights three times and then pause one second:
for (int i = 0; i < 3; i++)
{
digitalWrite(Player1RelayPin, HIGH); // Turn on Player 1 lights
digitalWrite(Player2RelayPin, HIGH); // Turn on Player 2 lights
delay(300);
digitalWrite(Player1RelayPin, LOW); // Turn off Player 1 lights
digitalWrite(Player2RelayPin, LOW); // Turn off Player 2 lights
delay(300);
}
delay(700); // Add this delay to the 300 milliseconds above to get 1 second
// Turns start with Player 1
TurnPlayer1 = true; // Player 1's turn
digitalWrite(Player1RelayPin, HIGH); // Turn on Player 1 lights
digitalWrite(Player2RelayPin, LOW); // Turn off Player 2 lights
PlayerTurnStartTime = millis();
}