K12 automatic gear shift button sticking

Have a 2004 K12 automatic. As it's getting on, niggling little problems starting to happen. Just recently the gear shift button has started sticking, it can sometimes take a couple of minutes of jiggling before it will let me shift from Park to Drive or Reverse. This morning it took about 5 mins. Once a gear is selected there's no further problem shifting between Drive, Reverse or Neutral. But it's becoming a bit hit or miss and I'm worried that at some point I'll eventually get stranded with the car stuck in Park. Can't fix it myself, is this a serious (expensive) problem if I take it to a garage? And what is the little black button (you could almost miss it altogether) at the back of the gear selector?
My Micra 2006 is having this same problem.
Please can anyone advice on what to do
In my original post I said 'gear shift button' - I meant gear shift lever. There is a little button behind the gear shift lever which if you depress it, releases the lever and you can then move it easily. But remember to keep your foot on the brake when you do!
Thanks PeterA. I have done this severally but it's not still pressing down
Have you ever disassembled/inspected and cleaned/lubricated it?
There might worn/damaged plastic part inside that prevents normal functioning.
I have cleaned/lubricated gear lever latch few times from my 1995 Chevrolet Camaro Z28S.
And added this small service to-do-list during this becoming winter season.
If the gear shift lever is difficult to move and needs some jiggling then it might be the microswitch on the mechanism that needs adjusting or replacing. This electrically stops the lever from moving but can be overridden by pressing the manual release button to the bottom right on the base (I think). In the end, although i bought a new microswtich, the lever on it just needed bending slightly and its been fine since.

More Info here .... https://bigblen.wordpress.com/2018/10/30/nissan-march-micra-stuck-shift-lock-repair/

and these are my photos from the comments ..... https://photos.google.com/share/AF1...?key=Mld4Qm4wcHNWWjJPbEV6dkpKal9pZVRuOFlLaVVn