The rear locking differential - if the car is fitted with one - is controlled by its own separate electronic module, connected to the transfer box control module as a ***** unit. This is the module that causes the padlock icon to change from green to red on the 4x4 screen, reflecting the actual status of the differential back there. If you have an open differential, you don't have this module. Whether the rear lockers padlock symbol on the display remains green all the time or changes to red whenever the center differential engages, who knows for sure at this point. It could in theory turn red, if the connections for the missing rear diff module were bridged on the transfer case control module of a car without rear lockers. Or it could stay green all the time. There's probably a tiny $0.10 jumper on a circuit board somewhere making all the difference...
When I went to one of those local Land Rover Experience promo events a couple of years ago I drove a "borrowed" Sport on the short demo course (it was inside a soccer stadium, leftover course from the X-Games, pretty cool!) If anyone has been at one of these, all cars are set to show 4x4 Info on the touchscreen during the course. When I went through a steep, sandy off-camber hill on the course, I noticed that both differential symbols on the monitor turned red, so I asked the guy dressed like Indiana Jones sitting next to me if the car I was driving was fitted with rear lockers, like mine. "No, all cars on the course are fitted with stock tires, no rear lockers. We need to show our guests what these babies can do with no options." "Why did the rear padlock symbol turn red just now?" "Because they both turn red on the display when the center differential locks. It's just the way the User Interface works if you don't have LRD." Maybe they think RRS drivers are dumber?

Or maybe Indiana Jones didn't know what he was talking about. My RRS has rear lockers so I will never be able to prove or disprove the theory.