I left my new Bluetooth OBD-II reader connected (to the parked car) and am wondering if it will drain the car battery?

try it and see, but I doubt it. Personally wouldn't leave something connected that doesn't need to be.

I don't know about the Jaguar but when I left something plugged into the port on my Subaru WRX, it drained the battery completely even though the device was off.

It probably will drain the battery.
But why leave it connected?
Your car will communicate with the OBD-reader only when the ignition is turned on.
So if you turn the ignition off the connection will get cut anyway and the OBD reader will still draw current.
(At least that is the way my OBD reader works.)


David

Depends on the specific reader. My HKS-Camp 2 remains installed in the OBD-II socket and causes no problems....then again it is designed for permanent installation.

For those who want to learn from my stupidity, the short answer is yes.

Bluetooth continues to transmit and you can indeed connect to it when it is merely plugged in even without the keys in the ignition - you cannot communicate with the ECU without turning the key to the ACC position, but you most certainly can drain your battery by leaving the device connected overnight