Painting streaks effect

Hi everyone,

I am trying to achieve an effect, I am sure it is really simple to do but I cannot figure out how to do it.

It is simply the effect of painting appearing on a wall with a brush. The brush doesn’t even need to interact with the paint, it could simply move over the wall and the paint appear right behind it as it moves. Something similar to this but on a bigger wall:

So far I faked it with a simple coloured flat cube that stretches behind the brush as it moves, but this doesn’t work if I want to move the brush sideways… I need this to be animated in Sequencer.

Any help would be really appreciated, thanks!