1997 Dodge Caravan - ignition relay problem?

I have a 1997 Caravan with the 3.8L 6cyl engine. The last few mornings, or when it hasn't run for several hours, (engine cooled) I get in, and the first attempt to crank the engine is met with nothing but the click of the keys turning the column switch.

Immediately attempting to start it again works, and it will start thereafter. It's when I first go to crank it after some time has passed.....I live in Florida, so cold weather's not an issue. Could this be a relay of some sort?