The small 12v one will be a Hella socket. Drop in to one of the CB shops and they will sell you an adaptor for Hella plug to cig lighter socket. Then you can plug it into 12v. Problem solved.
The Hella sockets in my Scania both have a black plastic ring around them, telling me that one is 24v with a max output of 300W and the other is 12v with a max output of 200W. This is usual with most makes of truck, if the ring is missing check in the hand-book. If that is missing as well, ask the CB shop to check what the voltage is. They will do it with a meter. In fact, get them to check it anyway, another driver may have re-wired it for some reason and could easily have done it wrong. Running your expensive gadget on the wrong polarity will fry it.