On the MKX there is no access panel on the side of the shifter. There is an access panel in the compartment under the center stack of controls where the usb, sd card, a/v connections are and it's location is described in the MKX ownwers manual, however when you remove the access panel there is no "lever" as described in the MKX's owners manual or button to push. The only mechanism to unlock the shifter in my 2011 MKX is just as I described. You are correct a momentary push of the start button does put the car in accessory mode however you cannot move the shifter with the car only in accessory mode. The only way to get the car in neutral is to start it (or use the process that I described). If you shut it off while in neutral the left display shows a message telling you to put the car in park. If you get out, shut the door, the message eventually goes out but part of the center display stays illuminated and continues to draw electrical load which would eventually kill the battery and does as described in some of the RV forums. I can assure you that on a 2011 MKX there is no button to push or "lever" to move as described in the owners manual. I've read and re-read the following instructions directly from the MKX owners manual and there is a possibility that the plunger that I described in my post is the "lever" they are talking about but in my car it can't be seen without a mirror and the only way to pull it out is hook it with your fingernail as the space is much to small to get your fingers on it. This may be just a case of a poorly written manual but the average person wouldn't figure it out with out some serious detective work.
BRAKE-SHIFT INTERLOCK
This vehicle is equipped with a brake-shift interlock (BSI) feature that
prevents the gearshift lever from being moved from P (Park) when the
ignition is in the on position unless the brake pedal is pressed.
If you cannot move the gearshift lever out of P (Park) with ignition in
the on position and the brake pedal pressed, it is possible that a fuse has
blown or the vehicle’s brake lamps are not operating properly. Refer to
Fuses and relays in the Roadside Emergencies chapter.
If the fuse is not blown and the brake lamps are working properly, the
following procedure will allow you to move the gearshift lever from P
(Park):
1. Apply the parking brake, turn the
ignition key to the off position, and
remove the key.
2. Using a screwdriver (or similar
tool), carefully pry off and remove
the BSI access panel.
3. Locate the brake shift interlock
lever in front of the shifter
assembly.
4. Apply the brake pedal. Gently
pull and hold the brake shift
interlock lever while pulling the
gearshift lever out of the P (Park)
position and into the N (Neutral)
position.
5. Install the trim panel.
6. Apply the brake pedal, start the vehicle, and release the parking
brake.
See your authorized dealer as soon as possible if this procedure
is used.