There are 3 points that are critical to a liner lock.
The pivot, the backstop pin/backspacer and the point the liner lock contacts the back of the blade. I'm sure you dont need a new liner from the picture on ebay. It is lining up at the correct side of the blade. When they get worn they tend to move over the to other side on dont work well, which isnt the case here.
I am assuming when you hold the handle in one hand and the blade in the other hand it tends to rock back and forth. The reason this is like that is because most likey the maker didnt seat the liner correctly. If its seated correct only the very top/tip of the liner contacts the back side of the blade. If the angle of contact is farther down on the blade, it will rock all day long.
There are a few fixes i use.
One that I do is use a carbonizer to put about a thousandth of an inch coating on the back side of the blade, liner lock face and backstop pin. All 3 surfaces equal to about 3 thousandths and can help. Or
You can take it apart and peen the outside of the liner split to stretch the liner so you have a better fit. Or
Or you can grind the back of the blade at the proper angle so only the tip of the liner on the top contacts the blade.
Of course when you start down this road the detent ball setting in the blade also needs to be reset because when you move the liner, the ball moves and tends to keep the blade not seating in the closed postion.