Well after trying the press the landrover button at the same time as you press the tailgate button sod all happened !!!! but I have found my key fob opens the glass bit but you cannot open it by hand, so at the moment its the only way I can open the top bit.
Button on dash does unlock the whole thing, its not a broken switch as it would not open when I use the fob.
So I have just given up and off down the pub......

If it opens on the fob but not the switch then its a faulty switch which is a common failure. Water gets into them 2x TDV6. SE and HSE. Both returned to sender with issues👀
TDV8 Sport HSE...... Gone. Loved it but it didn't love me!!
Now rolling in MY10 Fullfat TDV8 Vogue. Slammed it to go round corners🙈
Cruising daily #56 mph in a Volvo V8. 😱
Lots of other toys in the cupboard...😜

thanks Simple 1

Did the switch fix it? I have the same problem. One of my key fobs opens it but nothing else will. I've changed the switch too and that didn't do it. I'm thinking it's the wiring now  2007 Range Rover Sport TDV6 HSE- Cairns Blue with 22" Stormers

Yes the switch sorted my problem out, it was a bit damp in side so I cleaned it all out and sealed with a bit of mastic TDV8 2007 window tints, side steps.