Fam42, sounds like you may have grounded more than the radio parking brake wire. When you grounded the parking brake wire from the radio it should be disconnected from the car parking brake wire. Installation guide says parking brake wire from the radio is spliced into the parking brake indicator on the car. For the bypass you simply ground the radio wire without splicing it to the parking brake. If you ground it and its still connected to the parking brake indicator for the car you will get a light all the time.
So go back and check you are not connecting your grounded wires to the veh