Dispenser light doesn't come on automatically

As an electrical engineer, I would assume there's a switch on the activation lever that is supposed to tell the control board to turn on the light when you press the paddle to get ice or water. I know there's one on my old GE fridge and my new KitchenAid as well. Like yours, they both have a separate button on the control panel to turn the light on manually that's independent of the paddle switch.

So my best guess here would be that you've got a defective switch on the dispenser. Of course, it could always be a bad connection or wiring problem, but I'd start with the dispenser switch. Unplug it and short the wires and see if the light comes on. If it does, boom, you've found the problem. Unfortunately, Frigidaire doesn't sell that switch as a replaceable part; instead you have to replace the entire dispenser assembly as one unit. It's number 8 on this diagram.

However, given that it's a brand new appliance, it's going to be under warranty. So your first step before taking anything apart should be to contact their service department and explain the situation. Assuming they agree it should be working, they'll either suggest troubleshooting and/or repair procedures or send someone out to diagnose and repair the problem.