Tow/haul light issues on after every start have to manually shut off

What is your question?

Tow/haul light is on and stays on until manually turned off, when light is on it is steady, along with extremely hard start which has never happened, and a very low idle when in park sometimes I have to stay on throttle to not kill motor. One day it ran great idled great no issue with tow/haul switch or light. The next not. The battery is new this summer and just tried battery in beater car and it fired right up. Trying to teach the mechanic side of vehicles to myself and ask questions and learn. Any help, suggesstions or insight would be appreciated. Thanks! 02 Chevy Tahoe

What makes this problem better or worse?

When engines cold(winter in Wisconsin), or hasn’t ran for a few days.

How long has your 2002 Chevrolet Tahoe had this problem?

Three days and counting