Because it's likely that the battery's thermal management is working to either heat or cool the battery so the pack remains in an optimum temperature range for it's long term health. The battery's management may also be balancing the cells. This is normal.
I am assuming that you measured the 1200W draw, is that correct? How long did it go before dropping off? If OilerLord's hypothesis is correct, it shouldn't go on for too long before dropping to near zero. A 1200W load running 24/7 is absolutely not normal.
I have a meter upstream of my EVSE. The draw is zero when the car is fully charged. However I have only checked in the morning and an hour or so after I think it topped off, meaning I cannot vouch for how long it takes to stop spinning the meter.