I remember that thing accepting almost any input I gave it. But it was a few years ago now, so I’m not sure which way I had it.
From what Barry posted, it should respond to the DC trigger too. So full power should be fine.
Half power isn’t really 6V, your meter is averaging 12V and 0V and reporting 6V. If you put it on an oscilliscope, you’d see it flip between 12V and 0V spending half the time at 12V. I thought that might work better because it is close to a 12VAC signal, with a 6V offset.
Do you have the rambo plugged into the IoT relay? There are two ports that are on when there’s a signal, and two ports that turn off when there is a signal. I think you got it to work, which unpowered the rambo.