Could you please post a picture of the tucker in the top set? I've got the same set and I'm missing the tucker, and was not sure what it looked like.
The other Greist - Standard tuckers I've got mount backwards - but it looks like this one slips on from the front side.
Here is what your other set looks like in case you want to look for the missing items.
the pieces in the front were sold separately - not part of the basic set. The Binder is the foot missing from the top row - it does not look like you have the binder either - I've been watching for a set that has one.
On the tools, does the right one have a little hook with a latch? If so it's either a tool to help "fix" pulled threads in sweaters, or it's a type of bodkin - loop turner, and possibly had a handle at some point in time that broke and fell off.