2010 F150 AC HELP

As the title says, can someone help me out with my trucks AC issue.
2010 f150 FX4 crew cab V8.

The AC works fine and blows cold when it's on. However, it doesn't always come on when I press the power button for it. Instead, I have to wiggle a socket connection that is under the dash right below the glove box. I attached a picture for reference. It's the plug with yellow wires. Can someone tell me what this connection is and a possible solution other than wiggling or unplugging/replugging it? Thank you in advance!

 

Something needs crimped better under the tape id guess.

 

Thanks for your reply, I think I'm going to zip-tie the plug tighter, I was thinking of just replacing it but after adding some tape it's been working well.
I'd still like to get a name of that part just for future reference though.