A couple-three ways: you can animate a mask to look like an eraser, you can animate a shape layer and use it as a track matte, or you can make a mask path on a solid, animate the Stroke effect and use it as a track matte, too.
I would usually go with a SHAPE LAYER+TRIM PATHS+TRACK MATTE,
but if you're not familiar with those methods, then YES, you can 'keyframe with the eraser tool' (same as paint)
1. Double click the layer you want to erase to reveal it in the Layer Window
2. Select the Paint Brush/Eraser from the tools (top row)
3. In the Paint options, select CHANNELS=ALPHA, DURATION=WRITE ON
4. Paint the direction of your "erase animation"
5. You can keyframe the "START"% AND "END"% to time when your erasing happens.
Your brush stroke will now animate/erase your layer over time.
Check the layer's effect window or layer properties, and you will find many ways to edit the stroke you just made.
(you can edit the size of your brush, the start/end time of the erasing, roundness and spacing of your brush, and more)
If you want to get a little more advanced with Paint, you can "express" the brush stroke path to a mask path so you can easily edit your brush's path (and even animate it)