Nothing to erase, really. Even the eraser tool is just a generic brush tool that generates brush keyframe tracks like the paint tool. and therein lies your answer: Ideally you dig in the timeline and edit or remove those effect tracks, rather than adding more on top, which likely would require pre-composing, anyway. I would strongly recommend you read the AE online help on these tools, even more so since they are pretty old and have a lot of unique quirks. It works completely different than in PS. And to be honest, if you really want to do handdrawn animation, AE is the last place I'd look. Krita is free, PS has an animation timelien and of course there are commercial tools like ToonBoom that are much more suited for this kind of work.
If you spin down all the options on a layer that has Paint applied and some strokes you will see Brush 1 through Brush # depending on how many brush strokes have been made. If the eraser tool has been used you can see the same thing, one Eraser # for each eraser brush stroke.
Below the paths, you'll see basically the same options that you would find on a shape layer with a path and trim paths added. Start and End, Diameter (stroke width), and so on. Eraser paths paint on the Alpha Channel so if you are painting on an image or a solid you are going to poke holes in the layer. This will create transparency on everything below the Eraser path, including the layer you are painting on. I hardly ever use the eraser tool to control my brush strokes.
I will use the start and end values to shorten them, lengthen them, or make them appear to write on. If I need to put a hole in the middle of a brushstroke I'll duplicate the stroke and adjust the start and endpoints of both copies.
I would suggest that you add two strokes to a solid layer so they form an X, open up all of the properties in the timeline, and start fiddling with the controls so you can see how the brushes interact with each other.