Yes, this is all in place. Everything runs fine as long as I don't try to turn on the autoControls. While this is not a necessity, we would like to get it running eventually.
I did notice on the first page you linked, the lines of code actually read:
slider.controls.autoEl.depends('click', '.bx-start', clickStartBind);
slider.controls.autoEl.depends('click', '.bx-stop', clickStopBind);
Using depends rather than on. I tried making that change and simply got the same error stating slider.controls.autoEl.depends is not a function.