I've attached pictures of something that appears to be some sort of brake controller. What is this used for? I don't think it is electrical.
I believe that is an electric trailer brake controller, it has too many wires in it not to be electrical. The steel line in the side should be hooked to the hydraulic brakes on the truck so that it applies voltage in proportion to the pressure you put on the pedal. The handle is used to apply the trailer brakes without the truck brakes.
Technique for shifting the 2 speed axle with 5 speed transmission Let's see if I understand this correctly. The red knob on the stick shift when pushed down sends a signal to the axle to get ready for a shift to low range; when pulled up it sends a signal to the axle to get ready for a shift to high range. To make the shift, you can either let up on the gas pedal for an instant or disengage and engage the clutch or both of those actions at the same time. So, the technique for running through 10 shifts is from a standstill (1st low) push knob down - clutch shift and start moving; (1st high) pull knob up don't shift tranny - pedal shift or clutch shift; (2nd low) push knob down shift tranny; (2nd high) pull knob up don't shift tranny - pedal shift or clutch shift; etc. etc. What is correct? A clutch shift or a pedal shift when moving from low to high range in the same gear? When watching youtube videos of the shifting process, I haven't been able to see when the red knob is pushed down and it almost looks like it defaults to the down position but that can't be right. The fingers must be hiding the down push of the knob from view.
If you're experienced with how the rig drives, you can shift from low to high by simply lifting the throttle pedal. But if the truck is new to you, better to use clutch disengage as well, easier on the gears on the rear axle. Same thing when you hit a hill and have to drop from high range to low, use the clutch as well until you get used to the rig.