Inverter Installed - Open Ground?

I finished installing my new Victron 250w 12v inverter. I hard-wired it with direct connections to + and - battery terminals using 9 feet of 8AWG wire. There is a connection point on the inverter for a ground wire. The manual tells me that the "AC outlet is isolated from the DC input and the chassis." (They mean the inverter's chassis, not the trailer.)

My circuit tester registered the AC output as "open ground."

I tried running a ground wire from the inverter's ground connection to the trailer frame, believing the trailer frame to be the ground in this case. The circuit tester still registers "open ground."

First question - is any of this a concern?

Second question - why is it still registering "open ground"?

Third question - if I do need to ground it, how do I do so?

Thanks in advance.

-Speak