Interesting release mechanism on your Kline. Thank you posting the photo; looks like a good rifle, would you put up some more photos of the whole rifle? Would like very much to see it, as Klines are somewhat uncommon.
There are some variations on the toe plate release: One had the botton protruding through the toe plate, (probably the most common); there is the type you have; and there is a style similar to yours, but the upper end, toward the triggerguard, is not fixed and the rod is beneath that end. To open the box you push down on that end to engage the button. Many of this latter type seem to be weaker, and have broken over years of use.
There are also release mechanisms where the button protrudes from the top butt plate finial; there are those that have a latch type opener on the butt plate itself, by the lid; and there are some on which the button is located under a portion of the patch box finial, or the patch box side plates. Bedford County makers liked this and used it often.
There are others beyond this, some which have hidden buttons, screw heads, or a panel in the stock which opens the lid when depressed. Pretty ingenious folks those gun makers.
Hope this helps some-Dick