Hi Phil and Shannon, and welcome to the Alpine Forum and iRV2!
I've seen it work the other way around: if you manually turn on the wipers, the Smart Wheel automatically turns on the headlights. It's a safety feature.
Have you looked at the 2 Smart Wheel files on the Alpine Coach Association website in the Alpine Tech Manual pages? You might find some helpful info there.
Also, anytime you have an electrical issue that you don't understand or think is incorrect, you should turn off the 2 battery master switches and then turn them back on. This resets many things. (In the case of an issue with the Inverter, unplug the little modular "phone" cord and plug it back in.)
Mike and Mike (Michele)
2004 Alpine 34 FDDS