Dingoonity.org

Here is the thing - I'm generally using "mouse mode", because it's giving me more freedom in configuring the control (in many games, when you're using gamepad, game automatically assign the "control keys" (up,down,left,right etc.) and you can only configure "function keys" (such as jump/fire/etc), while with keyboard settings you can do almost whatever you wish.

BUT - in some games I could really use those R1/R2 or L1/L2 as keyboard buttons, to map them for more comfortable experience. Not to mention that I don't feel the need of having two buttons being equivalent of LMB and two buttons for RMB (it's really unnecessary), and that's how it looks in default settings.

My question is - how (if it's possible) can I make on  of the "pair" (preferably R2/L2) as keyboard keys? Preferably as any "not troublesome" keys which are not already assigned to d-pad and ABXY buttons (arrows and WASD) in mouse mode?

No, despite the multitude of requests for this wasted mapping in mousemode to be changed, GPD seems uninterested in making it fuctional for gamers.  Most of us have given up on it altogether and use alternative software for mapping gamepad to mouse, leaving the device in xinput mode 24/7.  Steam beta has released support for its controller config for nearly any gamepad now, and it works pretty well.  Some bugs need to be worked through and there's an initial effort required to get things configured, but its the best solution today.  Controller Companion is a nice 2nd place, with great support for gamepad to mouse/keyboard (aka mouse mode) configuration, and profiles for the desktop and per game.  Will launch on startup as well, so its actually my favorite solution so far.  Finally, there are other tools like xpadder, pinnacle (pure garbage), and some other package people are really pushing thats also free.  I think steams solution is the best of the group, as it allows full remapping of the controller to work in almost any scenario, including remapping the physical buttons to be other gamepad buttons.  Try them and see what works best for you.  Any hope of getting the mouse slider on the gpd to do something useful is probably wasted energy, after 3 firmware updates, it doesn't look like its happening.  The situation got worse in v23 when they overlapped the l3/r3 buttons as mouse buttons as well for no apparently good reason. 

Since these kind of things seems to be done by firmware update, I doubt we'll get an easy userspace way to configure that soon... This controller compagnon seems the way to go if you can't use an external mouse and the controller in another mode...