Some clarification is in order.
First - the four wheels only flash when 4WD is being engaged - and this only happens when you shift from 2WD to 4HI (a change to 4LO does NOT engage 4WD since 4WD is already engaged!). You can change from 2HI to 4HI and back when your vehicle is moving but they recommend that you do it below 100km/h. Many recommend that you ONLY do it when you are on a loose/slick surface and even then only when you are likely to lose traction. You don't need to have your foot on the brake, or have the car in neutral for this.
Second, the change from 4HI to 4LO requires that your car is STOPPED with your foot ON the brake and the gearbox in neutral. When you switch it over and the conditions are correct you will hear a thunk from beneath the car as the drive ratio changes. 4WD is already engaged at this point (normally) so the four wheels should have already been solid and should remain that way.
My initial guess on the problem here is the servo or its electrical connection. There are a couple of relays in the engine bay for the transfer case - open the little box that's behind your battery and have someone listen to it while you engage from 2WD to 4WD - the relays should click. Remove them one by one, inspect the feet, reinstall before removing the next one. This should clean any contacts that might be dirty.
Failing that, I'd guess the servo has failed - it's happened before. Also had someone rip the wires out of theirs while on a track, and they used a flat screwdriver to engage 4LO - turn the mechanism 90 degrees to engage 4HI and then a further 180 degrees in the same direction to engage 4LO. You could try that just to make sure the mechanical stuff works, then while you're under the car (with the car up on stands preferably) check the servo works with a helper in the cabin while you have the servo in your hands.
