Although it's usually may appear safe to "share the ground wire" between the 12vdc and 120vac systems, it's really not a great idea.
If somthing goes wrong with a gadget plugged into that 120vac outlet, it could lead to 120vac being connected to the "ground" wire.
That makes one end of it 120vac, and the other end "zero" (or, on inverter, possibly 60 vac).
Until the breaker or GFCI pops, that 120vac is being connected to whatever 12vdc device is "sharing" the wire ... which may propagate "upstream" to other 12vdc devices on that circuit or (indeed) positive bus bar.
Running a "private" ground for the 12vdc lights avoids that. The two "grounds" only meet at the zero volt end of the 8 gauge wire.
--dick