I think it means ignition needs to be on and it has to detect an open or short for a second or more before the fault code is set.
It's not a problem with the VVT signal it's a problem with the OCV+, OCV-, OCV2+ or OCV2- signals which is part of the VVT-i system.
It may not be a wiring problem, it's the first thing to check. Could be a problem with a VVT-i solenoid or the engine ECU.
This may explain your CO problem and also why your engine doesn't seem to run properly at high rpm.