I am pretty sure I put the info on the switch I used in on of my posts. The switch had 3 connections. Center connection is for power. Connect the fold out wire from both mirrors to one side and fold in to the other side. I installed the switch in verticle orientation. When I press and hold my switch up it closes the mirrors and down opens them.
I don't use remote start very often. But I just did and mirrors remain folded. The mirrors do not unfold with remote unlock or with the exterior buttons on the door handle. Once in the truck pushing the brake pedal and the start button the mirrors remain folded. Using the switch the mirrors can then be unfolded.
When you enter the truck after the remote start you have to step on the brake and push the start button. After that you should be able to use your switch to open the mirrors.
You are correct the original author did purchase the wrong size. He told me he feed the conductor through the connector and folded it over little bit. I did the same and it is a lot easier than using a connector.
I did not connect mine since they add little value. You would need to determine the correct pins at the mirror control the lights and then connect them to the correct K9 module. You need to use the GM ELECTRICAL INFO at https://www.gmupfitter.com/wp-content/uploads/2021/05/20_Sierra_1500_Electrical_Body_Builder_2019JUN20.pdf