Dimmer won't work when connected to power inverter

I successfully tested an 18ft long section of rope lights (Hunter brand) and a 3-stage touch dimmer in my house before taking out to install it in my RV. After plugging it into my 12VDC to 110VAC power inverter it just has one brightness level which is maximum brightness. Once its on, I can't turn it off again without unplugging it. I tried using a standard incandescent rotary dimmer with the exact same results. Why is this happening?

Why does it work properly on 110V 60Hz household current but not with the power inverter? Thanks.