When InDesign creates a package it inserts a file named Instructions.txt listing the fonts and artwork included. Back in IDCS4 days ID didn’t try to include CJK fonts, but for some recent jobs IDCS6 did package some Adobe CJK fonts; oddly, Instructions.txt specifically said they were not in the package even though they were. Accurate or not, at least ID reported on all the fonts needed. So I’d start there.
Chinese fonts vary dramatically in the number of characters they include, nowadays ranging from ca. 20,000 to several times that. This renders “SC” and “TC” pretty meaningless, and “dreaded pink boxes” are simply a fact of life when changing Chinese fonts or for text with any sort of complication.
There is a very handy InDesign script for identifying the missing chars., as discussed at https://forums.adobe.com/thread/1037284 — see the link to Peter Kahrel’s improvement near the end. Once you know the missing chars.’ code-points you can use Windows CharMap to confirm whether a particular font includes them. Or you can download Andrew West’s splendid BabelMap, where the Fonts/Font Coverage tool can list any installed fonts containing a specific code point or all the chars. in a pasted-in text snippet.
A major reason for “dreaded pink boxes” has been that Chinese fonts generally offer few alternate weights, and those only in small character sets. Two open-source projects now address this, with 64K chars in seven weights. Google makes them available as Noto CJK, though I use the Adobe versions named SourceHanSans and SourceHanSerif. I still prefer Adobe Ming and Adobe Song (in that order, depending on the chars. I need), but I’ve used SourceHanSerif for heavier weights or special circumstances.
Good luck,
David