Le Sabre No-Start

When temps drop below 20 degrees, occasionally my 97 Le Sabre with 125K miles won’t start after sitting overnight. Turns over okay, but when there is a clicking sound under glove compartment area, it won’t fire. If battery is disconnected for 5 or 10 minutes, then reconnected, clicking stops and it starts okay. Fuel pump and fuel pump relay has been changed. Battery terminals have been cleaned. Any suggestions?