599 Starter won't engage

I have a 2008 599 and occasionally there is a very long delay of up to 20 to 30 seconds before the starter will engage after pressing the start switch. Sometimes, it won't engage at all and I have to cycle the key and try again. Lately, when this happens I found that if I wait about 3 or 4 minutes and try again, everything is fine. The battery is fine and the starter cranks strong, and when it won't engage, there is no clicking or noise from the starter, but I do hear a relay clicking in the interior when I press the start button. Any ideas? I'm wondering if there is something with the immobilizer causing this.