My suggestion would be to draw a series of lines along that same path, think of it more like a star field simulation. An additive method instead of subtraction. You’ll need to store the location of the dots in an array and then calculate where to start and finish each line draw.
Then a function can advance the array depending on your speed.
I think it would be good to make it draw all of the lines as occasionally broken, to add to the depth feeling on a 1 bit display.
Not to throw a wrench in your works but there is also trees that go by on the side I think?
EDIT: No it’s bushes, there is a spinning air freshener.
and very bad edit of night mode:
RE-EDIT it’s probably better to prioritize the clock display than the door opening handle.
MORE-EDITS: You gotta make it so the player can enter their name
I’M NOT YOUR BOSS BUT: Make sure you have a title screen and a victory screen!