I just remembered why I prefer the location of the car's right
rear, just next to the roof:
When parking, it's the highest place to put the antenna. In most
of the world, people drive to the right side of the road. We
typically park the car on the right side of the street.

Whoops!
I was wrong. Let's shift this thing to the _left_ rear corner. My
reason was the least likely spot for the antenna to tangle with
tree branches when parking. That would be on the left, not the
right side.

I had to visualize this, and it just came clear while writing.

This position won't work with every car, of course. I last used
it with a '62 SAAB sedan. I mounted the antenna on a removable
cowl, which was pretty strong. I used a jury-rigged FM tuner
board in a plastic box that I'd patched into the AM radio. It was
important for me to have FM in the car so that I could listen to
my station on my way in to work, and especially, to see if the
person I was relieving was running the station on time or not and
if there were any technical problems that I'd have to deal with
on my shift. As soon as I could afford it, I replaced this setup
with a Blaupunkt that delivered superb performance and cost quite
a lot at the time.

Richard