I once made a slightly different rubber band gun that would very easily go "full auto".
It was a simple wooden yardstick.
At the front you stapled a strip of cloth long enough to reach the back of the stick
Below where you stapled that, you cut a V-notch in the "nose" of the stick.
Then you would cut notches about every inch from around 10" on up to around 20"
(the notches are on the "top" edge of the stick.)
Now pull the cloth over the stick, covering the notches.
In the V-notch at the front of the yardstick put one end of a rubber band. Stretch it back to the first notch (closest to the front) you cut in the stick. Place it over the fabric and down into the notch.
Continue loading rubber bands -- in the front notch, stretch back, into the next notch on top.
Now the fun starts!
Pull the strip of cloth backwards. As you pull, it forces the last (farthest back) rubber band up out of its notch and it fires. If you pull slowly, you get one rubber band at a time.
But if you yank that strip of cloth --- FULL AUTO!!!