Efnfast, I think you may be confusing "bevel gears" with "dog clutches". The drive engagement system in the Cat 12's relies on simple dog clutches with 4 angled faces, sliding on a shaft into mating engagement, to provide drive to the selected area of the blade (or scarifier) controls.
The only bevel gears involved in the power control box, are permanently engaged in the power control drive system box, and in the drive mechanism to the blade lift gearbox.
The dog clutches develop wear over time (and through poor engagement techniques), so they need a lot more lever pressure to stay engaged. However, if the drive mechanism between the power control box and the blade area that you've selected to operate, has worn bearings - or has run low on lubricant - then the levers will start to kick back, and the dog clutches will then be difficult to keep engaged.
The drive to the blade lift/lower mechanism goes through a couple of 90° bevel gear driveshafts, to a worm drive gearbox, which is mounted on the front panel of the cabin. The blade is normally locked in position because of the worm drive - the big bull gear can't turn the small worm gear when pressure is applied from the blade lift/lower shaft.
In addition, there are "anti-creep" brake mechanisms inside the power control box drive systems, that prevent movement of the drive once the levers are released.
The first thing to check is that power control gearbox and the worm drive gearbox have the correct level of oil in them. The second thing to check is that the (aluminum) worm gear is not badly worn (as they tend to do - and mostly in one area, over approximately one-third of the gear). A large quantity of aluminum particles in the oil of the worm drive gearbox is not a good sign.
The next thing that needs to be checked, is the condition of the bearings in the bevel gear driveshafts to the worm drive gearbox. Once again, many steel particles in the gearbox oil are not a good sign.
Then, the next thing to check is the bearing where the big horizontal lift arm is supported by the arm welded to the main frame. If that bearing is seriously worn, then there is a possibility you will get binding of the drive in the blade lift system.
I'd be checking all the drive mechanism system for severe wear and associated binding, before I started pulling the control box apart to recondition the dog clutches.
The old "knucklebuster" Cat 12's are a good grader, provided you keep wear out of their many complex mechanical drive systems.