Yes, the engine should be off.....and if the steering wheel is unlocked when you turn the key to off, then it doesn't need to be in ACC.  I would definitely check this before actual towing.  The steering wheel needs to be UNLOCKED during towing or you'll destroy your front tires.
Some vehicles you can turn the engine off and leave the key in "off", but NOT pull the key out and the steering wheel will stay unlocked.  Once you pull the key out, the wheel will lock.  However, when the key is in the "off" position, it is then released and can actually fall out of the ignition due to vibration when towing.  Best to leave in ACC.  Unfortunately, leaving the key in ACC can actually leave power on to some accessories...radio, nav, etc and can/will drain your battery.  That's why on some vehicles you have to pull a certain fuse that will turn off the power to these accessory items.....some you have to pull the neg cable off the battery itself.
I have no experience with a Taurus, so hopefully someone who has will add more to your post.
Ron