Jibber-Jabber
Answer: ALICE
Summit Wei

We are presented with a bunch of clues that make frequent use of vague words like "something", and a crisscross grid. These clues are clearly not solvable as is, so we need to figure out how to solve them. The flavortext uses the words "looking glass", which alludes to Through the Looking Glass, and combined with the title containing the word "Jabber", we can infer that this puzzle is about the poem Jabberwocky, which is famous for its use of nonce words.
If we take all the words that Carroll made up in Jabberwocky, we can roughly assign them to these clues. For instance, "Something that something went (hyph.)" strongly indicates SNICKER-SNACK. It turns out that the clue answers are ordered by length and then alphabetically, which makes them easy to solve. Solving the clues can also be skipped after making the initial aha; the clues are primarily useful to make sure that the words you choose match the intended (e.g. JUBJUB BIRD instead of just JUBJUB). The list of clue answers is as follows:

Clue Answer Quote from Poem
Something that some things do (along with something else) GYRE slithy toves did gyre and gimble
Something that describes some things that did something MOME the mome raths outgrabe
Somewhere that some things did two things WABE toves did gyre and gimble in the wabe
Something that some things were MIMSY All mimsy were the borogoves
Some things that did something RATHS the mome raths outgrabe
Some things that did two things TOVES slithy toves did gyre and gimble
Something that someone says (part 2) CALLAY "Callooh! Callay!" He chortled
Something that some things do (along with something else) GIMBLE slithy toves did gyre and gimble
Something that describes some things that did two things SLITHY slithy toves did gyre and gimble
Something that describes something that someone did UFFISH And as in uffish thought he stood
Something that describes someone BEAMISH my beamish boy
Some time BRILLIG 'Twas brillig
Something that something did, along with something else BURBLED came whiffling... and burbled
Something that someone says (part 1) CALLOOH "Callooh! Callay!" He chortled
Something that describes something that someone did something to MANXOME the manxome foe he sought
Something that someone did CHORTLED he chortled in his joy
Something that describes some time FRABJOUS O frabjous day!
Something that describes something FRUMIOUS the frumious bandersnatch
Something that some things do OUTGRABE the mome raths outgrabe
Some things that were something BOROGOVES all mimsy were the borogoves
Something that something was doing through something, along with something else WHIFFLING came whiffling through the tulgey wood, and burbled
Something that someone was doing GALUMPHING he went galumphing back
Something that someone says to do something about JABBERWOCK Beware the Jabberwock, my son
Something that someone says to do something about (2 wds) JUBJUB BIRD Beware the Jubjub Bird
Something that something did something through (2 wds) TULGEY WOOD came whiffling through the tulgey wood
Something that someone did something by (2 wds) TUMTUM TREE So rested he by the tumtum tree
Something that went something (2 wds) VORPAL BLADE The vorpal blade went snicker-snack
Something that somebody did something with (2 wds) VORPAL SWORD He took his vorpal sword in hand
Something that someone says to do something about BANDERSNATCH shun the frumious bandersnatch
Something that something went (hyph.) SNICKER-SNACK The vorpal blade went snicker-snack
Now, we can place these answers into the grid. This can most easily be done by starting with the longer words (in particular, the two 12-letter words, which can be distinguished by their crossings) and built from there.

From top to bottom, the gray letters spell WHO READS POEM. Within the book, that person is ALICE.