2012 z71 4x4 crew cab 3.7 I5 auto tranny , 66K miles, not a single repair needed. oil, filters and tires. Still running on original brake pads !
The big black box on top you mentioned, the one you must remove to change spark plugs, it has a black rubber "Vent Hose" that comes off with it from the back side. It is about 4" long with bends on each end. Over time, with oil fumes passing thru it, it gets soft and may not plug in well at each end or can even develop a fold or hole in it. It needs to be somewhat rigid in order to fit on nipples at each end, as you can't guide it on by hand. Mine had developed a fold/hole in it, and felt mushy. I ordered one from Auto Zone, they list it as "Vent Hose", and had it the next day. Cost about $8. Small amount of oil fume had collected on the black box that lead me to investigate. When box was off I cleaned it and it is fixed. Idle is also much smoother. Sounds like your issue.140k miles and running better after changing the sparkplugs. From the air filter box to the throttle body, that big black box on top of the valve cover seems to have a tiny trace of oil. But, it was clean otherwise. It idles just about 550-600 RPM, from what that tachometer needle shows on the dash. That seems kind of low to me, from all vehicles I have ever owned. I did change the oil with full synthetic Castrol for high mileage vehicles. I had Jiffy Lube do a coolant replacement. I wouldn't recommend that. Whatever they did do, over pressurize the system or put the wrong type of coolant, caused the radiator to leak along the top tank seam. I replaced that with a new radiator and cap. This also helped me learn that the radiator shroud being able to come apart in three pieces, held together with special little clips, which I ended up losing one. No big deal, I was able to use a zip-tie to keep it together on the one missing clip.