05 suburban stuck in tow/haul but light is not on

[Mark in SFlorida]

My first post - I have a 05 suburban.  116,000 miles.  Just acquired it and dont know much history.  It shifts oddly but firmly.  No apparent slip.  But it acts like it is in tow/haul mode shifting late like 30 mph out of first gear and does not drop into overdrive.  The tow/haul light is NOT on.  But it does come on when I push the button on the shift lever.  

 

A code came on that said "shift solenoid A stuck on"  code 472.  I cleared it and it has not come back on but still does same symptom.  I assume there is a timer.

 

A mechanic (according to recent records) replaced the solenoid but apparantly that did not solve the problem.  Trans oil has been replaced recently and filter too I assume when solenoid was replaced.

 

Car did sit for 1.5 years and I dont know if it was driven at all.

 

I checked the tow/haul wires at base of shifter.  All looks good.

 

Any thoughts?  I am stuck!

Thanks ahead of time, Mark