Does your 105 have manual locking front hubs? If so, and considering the "H2" option on your selector lever, I'm guessing your vehicle doesn't actually have a centre differential. Or at least not one that can be engaged/disengaged.
One way to check is to jack the wheels off the tarmac and spin the propshafts with the selector lever in H2, and again in H4 (I'd do it with ignition ON in case the lever also initiates some electrical actuation). If spinning one propshaft always results in positive drive to the other propshaft, then there is no centre diff.
Alternatively, it may have a CDL installed, but it's been actuated to the locked position and is now permanently engaged (which is a possibility for a UN vehicle. i.e. a cheap and lazy way to make a part-time-4WD out of a constant-4WD driveline, once you add manual locking hubs)
If the vehicle did have a centre differential it wouldn't provide drive to the rear axle with the front hubs unlocked, until the centre diff was locked. It's the same when you remove the front propshaft from a constant 4WD model; you need to lock the CDL to send drive to the rear. The centre diff sends all torque to the wheel/axle/propshaft with the least resistance unless it's locked.
Kamran Khan states that his vehicle illuminates the CDL light (yellow?) when he selects 4WD. You say you have a green light. I'm thinking both are best described as "4WD Engaged" lights, not CDL warnings. Toyota may have gone to the green light to reduce confusion.
Part of the UN-spec build might be to install the sensor on the transfer case (so oil doesn't run out) but cut the wires so there is no erroneous dash warning (in your case a green 4WD light PLUS a yellow CDL light). Also saves having to supply a specific blanking plug for a limited quantity of UN vehicles.
And, don't assume all the UN-spec 105s were built the same.....