Do a search of the threads here about the Big 3. Lots of them and read thru them. The ground problems can cause so many things. Some of the stories here make you think aliens have taken over your rig. The starter still trying to engage with key off and out may be a starter relay in the fuse box under the hood. The cover will identify the location and you can see if there is another relay that is a match and swap it out and see if that fixes the problem. The starter is getting power feed somewhere for that to happen, with key off and out. If the starter drive is sticking that will damage it and will shorten the life of the starter. I would do the obvious known problems/weak spots first of the grounds and see what happens.
Yes it happens sometimes when the vehicle is started then seems like everything is out of wack turn it off and the starter is still trying to start if the key is left in on "on" it has a chance of starting itself which it has just a couple of times but I will study the big 3 threads for sure
Okay this evening my neighbour said he was walking his dog this morning and it was trying to start but I woke up late and did not even go outside yet to do anything with the yukon around the time he said and also mention the previous owner was pulling the starter fuse alot to prevent use of vehicle
I saw that plug hanging out of the grill. You must live somewhere very cold. If in the rust belt, then all grounds are essential to check and reseat.
As for the code for the 1-2 shift solenoid. They fail occasionally, so it could be that easy and they are not expensive. I want to say that you can even change that solenoid without removing the valve body, but someone will correct me if that's not true.
If you are refreshing it anyway, you should be doing transmission fluid, filter and possibly something like the TransGo shift kit for the valve body. That will replace old springs and improve shifting.
I would inspect the separator plate as well while in there, these are known for the check balls punching their way through the plate. On mine it was the check ball for 1-2 upshift was almost pushed through causing erratic shifting.
Yes I live in Canada haha very cold, but I bought a rebuilt 4l65e with a corvette servo, accumulator work, hardened sunshell, a rebuilt torque converter so since my engine light wasn't working I didn't know my transmission was sending a code till I took it in for an alignment and asked some questions.
I contacted the person I bought the transmission from he is very sure it's not his transmission that is causing the problems but I'm hoping it's only the solenoid or the harness if he didn't put a brand new one in, I would expect what you suggested would be the case if the vehicle had it's original transmission, the original was toast from previous owner