Please see this image from an old desk I have inherited:
I have concluded that these holes need dowel/barrel nuts and then at-most an M8 bolt that shall be screwed into them. It is also possible to use M6. The height of the dowel nut must be 14mm. I do not have the parts that are required to assemble this and am trying to figure out what I need to buy.
The hole has diameter of 15mm. I am unable to find dowel/barrel nut that has this diameter. All the ones I can find are 10mm - 12mm. Now the question is what to do.
One idea I have come up with is, buy wooden dowel stick with 15mm diameter. Cut it and put it into the holes. Use wood glue and then sand the surface. Now, drill a small hole that exactly fits the smaller 10mm metal dowel/barrel nuts and another hole for the bolt.
Since these holes are on the side of the desk, I do not see any reason why a cam-lock would be fit into here. Thus, I have ruled out the cam lock.