I am having a hard time trying to figure out the mechanism of 4-aminothiophenol going through the EDC/NHS coupling reaction. Where the 4-aminothiophenol that is linked to a gold nanocage will be crosslinked to a protein either in the c terminus or n terminus.
From the wording of your Q, it seems like the thiol will be interacting with the gold surface prior to conjugation? This may direct the EDC reaction more towards the amine, but you'll just have to try I guess. The 4-aminothiophenol doesn't give you very much 'spacing', but it may be okay depending on the application.
I'm not sure how you will get directed attachment at either the N-terminus or C-terminus with this chemistry, as the amine will react with carboxyls which are likely to be found throughout the protein.