How to make a component of the precomp appear on the precomp?

This is definitely one way to achieve what you want (also, note that you can lock viewers at the top-left, so they don't switch around on you, and you can click the play button at the bottom-left, so you can always preview a specific viewer), but there's an even cooler way if you're using CC 2018!

Are you familiar with Master Properties?

If you're using CC 2018, try this:

1) Open the Essential Graphics panel. This can be done a couple ways

1. Window>Essential Graphics
2. Even easier, right-click in the empty area of your precomp's timeline and choose "Open in Essential Graphics."

2) With the EGP open you can now have a few options

1.     Click the button that says "Solo Supported Properties" to show all properties that can be added to the EGP, but this can make your timeline really unruly.
2. Reveal the sliders you want to control in your main comp in your timeline, select them, then right-click and choose "Add Property to Essential Graphics. You might be tempted to just start with this step, which will work if the EGP isn't open (so there's even a third way to open the EGP and then do this all in fewer clicks), but if you have another comp open in the EGP, then you'll get an error.
3. Reorder and rename your Essential Graphics properties to your heart's content.
4. Here's where the magic happens: Go back to your main comp and twirl your precomp open to see a new option called "Master Properties." Under that heading you'll now see just the properties that you added to your EGP.

This is an incredible new workflow, and it's easily one of my favorite additions to After Effects in the last 10 years.

Here's some more official info about Master Properties: Create Motion Graphics templates with Essential Graphics panel

This is also part of the same workflow to create Motion Graphics Templates for Premiere Pro, but it was expanded to be incredibly powerful inside of AE.

And here's a School of Motion tutorial about Master Properties: https://www.schoolofmotion.com/tutorials/master-properties-after-effects