Ahh I remember Dad doing that too, he just described it as he had to "lock the wheel". I think there's a button for the wheel lock now but his gearbox isn't as techy looking as yours.
He still likes his jungle hikes but I don't think he misses doing all the manual stuff with the cars much as he is pushing 70.
Yeah, some have buttons, mine is a knob, the one above the terrain selection one in the image.
I think I'll be the same as your dad as I get older, four wheel driving takes effort, not so much driving, but when one gets bogged it's a lot of work to extricate oneself and that's not an old man's game. (Not that I'm old yet, but you know what I mean.)