Sure, all the black wires need to be grounded. They multi-plug into black wires in the harness that eventually ground to the frame and battery. You may find broken/cut wires, damaged/corroded grounding lugs, poor/corroded/missing lug connections to frame. Most electrical advise on this forum recommends thoroughly inspecting and cleaning all connectors, including grounding lugs. Sage advice considering the age of these machines. Poor/missing grounds, floating grounds, ground loops, intermittant grounds, hi-resistance grounds, can lead to all sorts of bizarre things.
Back when the first prototype fibreglass Corvette was built, nothing worked right. They used assembly line workers, who did things the way they were taught, and screwed the grounding lugs into the fibreglass...