Time to have a look under the truck to confirm that you actually have diff lock equipped differentials.
They will have an actuator and some wiring next to the actual Center section of the differential where the drive shaft goes into it.
Strange that the Center diff indicates locked but you get no flashing lights for the front and rear differential locks.
Could just be faulty bulbs.
Chock two wheels on one side of the truck. Put the transmission in Neutral, Jack up one wheel front and rear on the same side,lock the Center diff. Try to rotate the wheels that are jacked up.
If they rotate a bit and then lock up then the Center diff is at least locked up.
Put the the front wheel back on the ground and jack up the other rear wheel.
Try to turn the rear wheels. If they rotate the same direction they are locked. If they rotate in opposite directions they are not locked.
Same for the front wheels.
If you have the gear you can jack up all the wheels and if everything is locked then all the wheels should rotate the same direction.
When you are trying to get the wheels to lock in a driving situation it can take quite a bit of time for them to lock because the splines inside the diff have to line up and that requires some difference in rotation of the left and right axle in the diff Center. The front will often lock before the rear as steering input increases the differential speed between the wheels.
And finally it is not uncommon for the diffs to be locked and the indicators to continue flashing because the switch contacts get dirty in the diff locked sensor. They are a simple plunger switch that is used in many Toyota transmissions as a reversing light switch. The very small current that the diff lock ECU requires to turn the light from flashing to solid is not enough to keep the switch contacts clean.
There is a thread somewhere on Mud that will tell you how to fix that problem.
Georgetlc also used to have this information on his web site.
Sarmajor, you posted above that "And finally it is not uncommon for the diffs to be locked and the indicators to continue flashing" Just as an FYI the OP stated in his first post that when he turns the diff lock dial, he's getting nothing on the dash, no lights at all for the front and rear diff locks.
Been there and done that. Forgot to plug mine in a couple of times after replacing things behind the dash
It is a right bugger to get that plug back onto the switch without pulling a bit of the dash out.
Sarmajor, you posted above that "And finally it is not uncommon for the diffs to be locked and the indicators to continue flashing" Just as an FYI the OP stated in his first post that when he turns the diff lock dial, he's getting nothing on the dash, no lights at all for the front and rear diff locks.