I would forgive you for thinking that reverse and backup meant the same thing, but in this case they don't. The previously discussed beta reverse valve prevents the propellers from going into beta or reverse blade angles unless the pilot wants them to. The beta backup valve is a backup system, designed to save the day if the beta reverse valve fails.
The beta backup system consists of two microswitches, one on the propeller feedback ring, tripped when the propeller blade angle drops below 9 degrees, and one on the power levers. The information I have suggests that there is one microswitch shared between the two power levers, and that sounds vaguely familiar, but I can't remember whether it's in the left or the right power lever. Perhaps there's one for each power lever only in the newer models. At any rate, if the power lever handgrip has been rotated, selecting the beta range, then no power is available for the beta back up solenoid, so the signal from the 9 degree microswitch is ignored.
If the power lever has not been rotated, and the feedback ring indicates that the propeller blade angle has dropped below 9 degrees, then 5 A of current flows from the right DC bus, energizing the beta back up solenoid, snapping the beta backup valve closed. No oil reaches the beta reverse valve, so its failure to close doesn't matter. Oil supply to the propeller hub has been cut off. This, as you know by now (repetition is an excellent way to learn things) results in the springs and counterweights in the hub driving the blades to coarser angles. Once the angle is greater than 9 degrees, the beta backup solenoid snaps open again. If the beta reverse valve is still not doing anything, the blades are driven back towards fine and the scenario resembles children continuing to play after a stalemate in chess, with the two kings chasing each other back and forth, endlessly in and out of check.
The microswitch that senses that a propeller angle is less than 9 degrees also illuminates a blue beta light for that propeller, so the indication to the pilots of a beta reverse valve failure is a flashing blue light. If beta has been selected deliberately, and the propeller angle remains at less than nine degrees, the blue lights will remain illuminated and not flash. (Some models have amber lights instead of blue, but I don't care for them).
As part of a normal landing, after touchdown a pilot might twist and pull the throttles into reverse, using the power of the engine to slow the airplane. Immediately afterwards, the pilot would likely advance the throttles to idle in order to taxi but the blades would takes a few moments to regain the 11 degree idle pitch. To prevent the beta backup system from detecting this situation "ooh, grip not twisted, but blade angle less than 9 degrees!" and cycling unnecessarily, there is another relay in the system. This beta disarm relay is activated if a grip is twisted and the propeller blade is less than 9 degrees. It remains activated until the grip is released and the blades return to idle pitch. While activated it inhibits the beta backup solenoid and illuminates an amber BACK UP DISARMED light. Therefore, the pilots can expect that amber light to go on briefly immediately following a landing where reverse thrust is used. I assume that the BACK UP DISARMED light illuminates any time the throttles are not twisted yet power is not available to the beta back up solenoid.
Of course there has to be a way to test this mess, and there is: a BETA RANGE TEST switch for each power lever. Lifting the test switch bypasses the power lever microswitch, so that power to the beta back up solenoid is maintained even when the handgrip is twisted. So lift the switch, twist the handgrip and pull it back. The blue beta lights will flash as the beta backup solenoid keeps the blade angle cycling back and forth through 9 degrees, and the BACK UP DISARMED switch will flash on and off as it thinks power is being removed from the back up solenoid without the power grips having been twisted.
Beta reverse valve failure is very rare, as it's a simple mechanical system. It's more common for the beta backup propeller microswitch to fail, removing the backup protection or sending a false alarm cutting off the oil supply and necessitating an engine shutdown. I heard that my target company has obtained permission to remove the beta backup valve and fly without a net for the beta reverse valve, but I don't know that for sure.
And if you think these propeller lights are complicated, wait until I tell you about the Gulfstream One.