drawing a slinky

This is a very manual, convoluted way to possibly get what you want.

1. Click with the Spiral tool.
2. Set the Decay to 100% and enter lots of Segments (the more Segments the longer your slinky can be.)
3. Click OK

What looks like a circle is actually a Spiral that is spiraling straight down on top of itself.

1. With your Selection tool (V), click on one of the side bounding box points and drag inward to fake perspective.
2. Deselect the Spiral.
3. With your Direct Selection tool (A), select the four anchor points that make up the top layer of your Spiral. Click on the first point and Shift-click on the other three points to add to the selection.
4. Double-click on the Direct Selection tool, to open the Move dialog box.
5. Enter a small amount like .125" in the Distance field and press OK. This will move the first four point to the right.
6. With the first four points still selected, repeat by Shift-Clicking on the next four points that are now revealed. And keep repeating until you run out of segments.
7. You could experiment with Angle amounts to make the Slinky go up or down.

It sort of works. See attached. I added a Silver Gradient to the Stoke to make it easier to see the overlaps.

A brush won't respect perspective.

Do you need perspective? Please show how you want it to look. An example? Your initial drawing?