It could be (nearly) flush. Look at most any modern US Navy warship, their phased array radars are flush mounted with the hull (they just stick out a bit).
What about having it emerge from the tailgate somehow? Lots of people think the back end of the CT is the weirdest / ugliest part of the truck so having a pizza-sized plate back there might not be the end of the world. It could look like the tail of a stainless steel dinosaur. Maybe Elon can make it wag? I mean, you really want it to work in motion, just not once you're parked. Maybe not today, but think about when FSD really works and you can Netflix while rolling down the road.
I already signed up with Starlink a few weeks earlier about being notified, and then just today got a request for an exact location as they refine their start-up region priorities. Hmmm, is this how SkyNet becomes self-aware...? ("Ah'll be bockkk...")
I will be interested to see where they start, I shouldn't have put my bay area address. They have TONs of people here.