Nothing at all to do with the CTS, this problem, if getting 12v one side and 5v the other side your valve is knackered, as it is not doing what it should do, even though getting the required input from the relay(12v) and the ecu(5v).
To test simply disconnect and drop your idle speed artificially low to almost stalling, now reconnect the iscv, this should pick the revs up to correct idle, as it only raises the rpm above the base setting, if it doesn't raise the revs and you have the correct input, then it's knackered.
Kicking the shit out of it with 12v direct from a battery will make most duff ones move, as they are overpowered big time like this.
The 5V from ecu is a pulse, which in a million years you won't see on a digi multi metre, as it simply can't capture the fast moving changes of lecky pulses, osciliscopes are used for this.
tabetha