How can I find the ALT code for an Elisian?

You cannot "add", or any other way edit, the characters that get displayed with Alt+<number>. What it displays is the Windows Latin1 character in your current font, and the Latin1 encoding is always used. (I never tried but I imagine it uses the current "default" code page for your system. But I know of no code page containing the Combining Breve.)

And be careful when referring to GIDs! This number might be useful if you want to swap out characters in the same font (for instance, when replacing a standard character with an alternate version), but all of these numbers are unique for that font and they don't mean nothing when applied to another font – they are physical character indexes in the font file, and other fonts contain more or less characters, other alternates, ligatures, and substitutions, and in other orders.

But you are not limited to using Alt to enter "any" character. You can use one of the methods reported in https://indesignsecrets.com/type-any-unicode-character-you-want-in-indesign.php and its comments (be sure to read them all, there are a few valuable gems hidden in there) and/or in https://indesignsecrets.com/insert-a-character-by-unicode-or-gid.php .

͜ - Unicode codepoint lookup/search tool

There is no character or glyph that is called ‘elisian’. So we all wonder what you mean...

What the heck is an "Elisian"? You may be misspelling it because a Google search of that provides no answer I could figure out.

And what do you mean an ALT list. It this a Windows keyboard shortcut? (Sorry, I'm a Mac user).

What InDesign version? What operating system?