Welcome to the forum jclape!
That lever on the left side(when siting on the machine) is the kick starter...not a shifter...150's have a GY6 style engine(Honda Scooter) that has a CVT instead of a gear box. That rear end does have a reverse in it and its activated by that lever on the rear end..When its in the relaxed position(towards the back of the machine its in forward...When the lever is moved forward its in Reverse... As for a manual it will be easy to find a engine manual but one for the specific machine will be kinda tough...