While my DK45 may not be exactly the same as your CK2610, my arrangement does look like the diagram from xcgreen's post.
Mine takes about 10 lbs to push the lever down. If the 'splines' are not aligned, the lever only goes about halfway. Keeping a steady pressure will allow the diff to lock as soon as the splines do align; a wheel slipping as you describe should allow the pedal to go all the way down immediately. Otherwise, I just keep a steady pressure on the pedal, and as soon as a wheel starts to slip you can definitely feel the pedal drop & the differential lock. Just to get the feel, you might try it while driving in a circle (rear wheels turning at different speeds)
I can't imagine you would need to push with more than 15-20 lbs... Does the lever move at all? If not, it must be jammed. This seems to me something that is definitely covered by warranty...unless you have run over an object (tree limb), and have jammed something into the linkage.
To: MikeR 2018 when you release the lever (lift your foot up) the lock should release. If it doesn't immediately, it's because the differential is in a bind, turning the steering wheel left, then right (while moving, of course) should relieve the pressure, and the lever will snap up.