Seems to me that the chair can be on either side.
A hack rig is a three-wheel vehicle leaving two tracks, with only the rear wheel driving, and only the front wheel steering. Chair may be on right or left of cycle portion of outfit. According to the United States Classic Racing Association.
The
New Zealand Classic Motorcycle Racing Register Inc. Technical Rules specify, again,
Sidecar may be on either the left or the rightSteer a hack. countersteer a motorsickle.
Moooooooo over...
However, normal practice in the U.S., is to mount the sidecar on the right hand side of the motorcycle.