did you select the path with the selction tool before you exxpanded it there should be no reason that a brush stroke cannot be erased
BTW showing us the layer panel like that actually only tells you have layers but nothing about the art on the layers.
Also it does not look like that brush stroke is vector anymore it definitley looks like a raster image or some kind of grouping.
Expand the layer in the layers panel so we can see some information.
I did select the paths first before they were expanded. I am able to bisect the paths with the eraser as you have demonstrated but am looking to 'clean up' the stroke by erasing the bits that fall outside my drawing. I see what you mean: the paths become images after the 'expand appearance' command is used. Below I have expanded one of the paths. Maybe the only way is to use a clipping mask as Scott W suggests?
Basically, you're thinking of Illustrator brushes as if they were raster or pixel based like they are in Photoshop. They are not. You can not simply erase the "overspray" areas outside the keyline. That's just not how Illustrator brushes work.
You would be better served by either A) using shapes and filling them with a gradient rather than using brushes at all. Or B) add a clipping mask to hide the overspray appearance of the brushes.
The help files will explain Clipping Masks further. Using the brush+mask method will easily double or triple the amount of work needed to color any piece. Not to mention, eventually cause the app to get a bit slower becuase it will have to redraw all teh brush strokes as you add new ones. It's just not an efficient way of working much of the time if you want hard edges on shapes.
Essentially, you're expecting raster-based results in a vector-based application. You need to reevaluate your workflow.
Of course, you could always take your vector keyline into Photoshop and paint color there in the manner you are attempting. That's what Photoshop does.
If you use shapes and need to work this way, and I agree with what Scott says using shapes might be your way and clipping paths are a good way but a better way for you to work is in a more visual and approach.
The feature is still in its infancy compared to the masking feature in After Effects but here goes.
1. Draw thye shapes
2. Select it and near the bottom of the Tool Panel seeelct Draw Behind or Draw Inside (the difference is if you draw behind and move the shape what's behind stays put if you draw inside and move the shape the what's drwan inside moves with it)
3. Now take any brush or drawing tool and brush away like crazy and it will be masked (you can also paste into or behind the shape now including images and vector art)
It is a very handy feature. If you are use to making clipping masks it might be hard to change and clipping maks are appropriate in many other ways.
I think the real problem here is that there are better ways to achieve the desired results. And using masks for every little piece will probably slow you down too much, since working with masks takes more clicks than what's desirable.
In order to create the seahorse's gradiently shaded belly segments I recommend a simple Gradient Fill, or Gradient Meshing.
And if you don't like how that works out for you, why not just use Photoshop?