Ah, this is interesting. I think you've found a bug! Contraptions should not be able to be pasted inside of other contraptions. It seems like it's possible, in the current version.... but if you save and reload the deck the nested contraptions will be gone.
I think it's still pretty easy to do what you wanted to do, though.
The eye contraption is relatively simple so it's very possible to incorporate it into another contraption. Its just a matter of putting the relevant widgets and code directly into your other new contraption, without the "Eye Contraption" container.
For the sake of making an example, I built off the code snippet and ideas from Internet Janitor in the post above created new hidden button widgets inside of the contraption to define bounding boxes for the movement of each of the eyes.
So here's a new contraption that contains two moving eyes and an image in a canvas:
%%WGT0{"w":[{"name":"eyezample","type":"contraption","size":[116,142],"pos":[38,100],"def":"eye-example","widgets":{"canvas1":{},"pupil1":{"image":"%%IMG0AAUABfDw8PAA"},"img":{"value":{"text":["","i"],"font":["",""],"arg":["","%%IMG2AAQABAEQ"]}},"b1":{},"pupil2":{"image":"%%IMG0AAUABfDw8PAA"},"b2":{}}}],"d":{"eye-example":{"name":"eye-example","size":[116,142],"resizable":1,"margin":[0,0,0,0],"description":"A quick silly example for the decker forums. ","script":"on get_pupil do\n img.value\nend\n\non set_pupil x do\n img.value:x\n view[]\nend\n\non track_cursor img pupil box do\n pupil.size:img.size\n pupil.clear[]\n pupil.paste[img]\n c:box.size/2\n p:pupil.size/2\n d:pointer.pos-box.offset+c\n m:(c-p)&mag d\n pupil.pos:box.pos+(c-p)+m*unit heading d\nend\n\non view do\n i:first img.images\n track_cursor[i pupil1 b1]\n track_cursor[i pupil2 b2]\nend","attributes":{"name":["pupil"],"label":["Pupil\nImage"],"type":["rich"]},"widgets":{"canvas1":{"type":"canvas","size":[116,142],"pos":[0,0],"locked":1,"border":0,"image":"%%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"},"pupil1":{"type":"canvas","size":[5,5],"pos":[29,48],"locked":1,"animated":1,"show":"transparent","border":0,"image":"%%IMG0AAUABXD4+Phw","scale":1},"img":{"type":"field","size":[27,28],"pos":[-73,29],"locked":1,"show":"none","border":0,"value":{"text":["","i"],"font":["",""],"arg":["","%%IMG0AAUABXD4+Phw"]}},"b1":{"type":"button","size":[20,9],"pos":[26,48],"show":"none"},"pupil2":{"type":"canvas","size":[5,5],"pos":[72,46],"locked":1,"animated":1,"show":"transparent","border":0,"image":"%%IMG0AAUABXD4+Phw","scale":1},"b2":{"type":"button","size":[20,9],"pos":[71,46],"show":"none"}}}}}
The image in my canvas is wrong, obviously. And it doesn't do anything else you may have intended your contraption to do.... But, well. I hope this helps clarify why things were acting weird for you, and also maybe it gives you a way to move forward with your ideas.
Please let me know if you have questions about it, or if you need more help getting it to do what you want it to do!
(The pupil areas can be changed inside the contraption prototype by moving/resizing the widgets named b1 and b2. )