The HIGH and LOW are sensors for the where abouts of a disc. It is for a CD-ROM drive.
Here is the somewhat basic logic:
If sensor 1 detects disc, forward motor.
if sensor 2 detects disc, disc loaded. stop motor.
if button pressed, reverse motor.
if sensor 1 does not detect disc, stop motor.
(there are some else's and stuff missing, but you get the idea).
Oh. The motor is some cheep tiny little thing. Like a small CD-ROM motor basically
Will draw hardly any amps
As for your idea with a relay, would a one shot 555 timer work?
I would rather something programmable :/