It seems International had a similar set up in some of their mixer trucks - goofy shift pattern, and maybe reverse was on the stick farther away from you.
Splitting will depend on the situation IE: weight and grade. It’s not often I split the entire low side, I normally run through the bottom on low side then start splitting on top side. Think I’ve split the low side a few times starting on large hills loaded heavy (roughly 132k) I also have 2 speed rears but have never been heavy enough to need them.
The only time I used the low side of the rear ends was in Oregon mud. That kind of work is for young men.
At work we have a couple Super 10’s that came out of CA, they are fuel straight trucks with 4500 gal tanks, pintel hitch that pulled 5000 gal pup trailers. One is a 1995 KW T800 with a 3406e, and another is a 2002 KW T600 with an ISM. Also a couple Freightliner Columbia’s with MB’s and 10 sp Road Rangers with pintel hitch’s sitting in the fence row.
Ok good question thanks for asking, whether your running up the Rocky's, through emigrant pass, or hauling iron ore in a 193 tonne road train there will be times when you will strike an up hill grade it could be really steep or could be a very gentle slope, either way when your towing a lot of weight your truck engine will feel the strain this is where the gear changing comes to the table, if its a slight grade a simple split of the gear will be enough as the truck is not going to slow down enough to actually drop it down a whole gear. Yesterday I ran a load of Iron ore from the Wonmunna Mine to Utah Point along the way I had to go up quite a bit of a grade going from 18th gear back to about 8 th gear, this is where the gear changing skills comes into play, what I usually do on this kind of grade is keep the splitter on high and just jump two whole gears going from 18 th back to 16 th to 14 th etc, etc you do not have to change down every gear if its slowing up enough, you can miss multiple gears so I changed gears 5 times back to 8 th gear which was just enough to get me to the top of the climb I left the splitter on high which allowed me the one extra gear just in case 8th was not enough I would of then gone down to 7th. The process when splitting gears is quite easy actually once you've been doing if for a while, it can look hard for someone that's just used to driving a 10 speed. However as they say "practice makes perfect " All you do when changing down is flick the splitter back ease back on the throttle and then rev up or you can just rev it up higher it will work both ways without the clutch, alternatively flick the splitter back then clutch in throttle back clutch out rev up again. To change up a gear using the splitter while your accelerating flick the splitter up then ease back a little on the throttle then accelerate again it should change smoothly if you've timed it right alternatively use the clutch if your not feeling confident.