I found some listed for 120V but also found some on the HomeDepot website that have 5V bulbs.
It is still a 120V rope. A 120V buss runs the length of the rope. Short lengths of bulbs are wired in series to add up to line voltage and those short series strings are tied across the 120V buss. So the rope can be cut at intervals at the short length sections (usually 18" or 36" depending on the individual bulbs voltage). LED strings are basically the same only a diode is usually in the line cord that connects to the rope and the connectors are polarized. I have seen other variations but that is the 10K foot view.
As far as pfeffer, I'm WAGing a leak to ground somewhere on the rope, especially if he DIMs the Lamp Module. What he is seeing is close to my experience at a previous home.