HVAC Blower Motor wiring

I replaced the HVAC blower motor on my 2010 with an aftermarket one off of Amazon yesterday. It worked for about 10-15 minutes and I noticed it blew the air out much better than the OEM which was on its way out. During a second trip it worked for about 2-3 minutes and then nothing no matter what I had the setting on. Right before we got home I started smelling a burning electrical smell even though the setting was off, and upon removal of the new blower motor I could smell burning electrical under the fan and it was really strong where the wiring harness plugs in. The truck's wiring harness also smells like this but am hoping it's just a dud blower motor and not a short in my wiring.

How can I test the wiring harness with my multimeter to determine if the wiring is still good? I have a replacement blower motor on its way but would like to test this before it gets here.

 

I get 12v and about 8-9ohms on my multimeter when I have the leads touching the blue and white/black wires. I assume the smaller middle wire is what controls the blower speed. Is there any way to check that? I tried turning the dial to full in accessory mode, but am not sure exactly how to measure any continuity/resistance/voltage with the middle wire, and I tried every combination with the blue and white/black wires and nothing showed on my multimeter.

 

Got the replacement blower motor and good news is my wiring is okay. It's working so far but it was only a 5-10 minute test. We shall see if this new motor will last.