This is a non-answer/partial answer. Just assembling some thoughts and maybe getting the ball rolling?
atop the monument seeking jewellery //
this fake character is not the ordinary //
a trio, the misguided claim to possess //
their psychiatric health we must assess
Edit: This could be referring to Jesus (though Idk what monument he's on top of). He's "fake" according to a lot of people, he is representative of the holy trinity, Christians (the "misguided") claim to have him in their hearts or whatever, which would make them crazy if he's fake. "Seeking jewelry" could refer to the crucifix as a piece of jewelry.
watching you now, locked in solitude //
lose thoughts of it and gain gratitude //
data from it to be deciphered //
easy comprehension is what's desired //
This sounds like it's referring to the riddle itself, so the word here is probably something like riddle, rhyme, poem. This could also be referring to your computer, however, so it may be computer, monitor, screen... If I had to bet, I'd go with monitor, since when used as a verb, it means to watch.
to see your path, you favour no grin //
just follow the road by the grimalkin //
the agreeable ones pillage upon the salt //
those who fare, through billow upon holt
I have no clue what this could be about. A road that is "by" a cat, but not a grinning cat (i.e. Cheshire)? So... A road that is the name of a cat and is somehow related to Cheshire...?
low warm and high cool, the air will fight //
stay close within to avoid the smite //
as the exterior rips through the land //
the inner recess is tranquil and grand
I doubt that this could be referencing anything but a tornado. How it's formed, eye of the storm, destruction...
shot, the projectile changes thee //
elude, the meaning will till you guarantee //
no material can heal what once was neat //
subtle memories, dread a repeat
Complete guess, but this seems to me that it's referencing the structure of the stanza itself. As if you're supposed to rearrange the awkward syntax to make it "neat" again, then re-read it to figure out what it's talking about -- it'll elude you until you do.
the drum of life does symbolise //
one does not simply analyse //
broken only, lonely alone //
rejection wrecking leaving stone
Not a clue. "Drum of life" could be referring to something like a song or book called "beat" or "rhythm" of life. Alternatively, it could be referring to a sleep cycle, or "biorhythm".
yet true twice in benevolent violence //
one look only for it gains entrance //
an entity for life you obtain //
create anew a life to reign
This sounds like giving birth. Two ovaries, one sperm enters an egg, baby is made. Not sure what the word here would be... Birth, conception, baby, anything in between...
compelled by this to achieve //
yet humility intervenes, you don’t believe //
effects differ and subjects vary //
listen to this its not that scary
It sounds to me like the word here is encouragement, though it could also be something like advice. Encouragement compels you to achieve something, but your own humble views of yourself may make you believe you can't do it.
the board rides the pipe into the air //
high as a hawk, its quite a scare //
thou shalt address thee as a clue //
be thy plumber of thy loo
Right, so address yourself as a clue when you're cleaning out your own pipes. The board rides the pipe... Yeah. Lol Idk what this one is about, but it sounds dirty.
material of squander travels around //
within the confines, trapped and bound //
nowhere to go the water rises //
break free quickly no nasty surprises
Material of squander... waste? Waste within confines and considered to be "water" sounds like a sewer, which is enforced by "nasty" surprises. So... I'm guessing sewer here?
Germans sink within this vessel //
under the radar hoping to nestle //
place what you need before the knee //
take the verse and have some tea
Obviously talking about a U-boat. I'm not sure what you would "place before your knee" before praying over tea... But whatever that is, probably in German, is what we're looking for.
the Gothic did state the differences //
upon the vague instances //
for we were once another //
our rather angular brother
This is talking about evolution, but I'm not sure what exactly we're supposed to extract from it. I don't think "Gothic" refers to Darwin, and I don't know enough to guess any other scientist. Otherwise, we could be seeking evolution itself, or maybe homo erectus or one of his kin.
All in all, I find myself very... confused by this puzzle.
Monitor, Tornado, Biorhythm, Conception, Encouragement, Sewer, Evolution...
I don't see a connection at all. The only thing I can think of is that
...all of these words are supposed to be appropriate words that might make people feel uncomfortable, hence making them the "hardest to verbalize". (Conception, Masturbation, Sewage, Homo Erectus...)
But I'm 99.9% sure that I'm miles away from the actuality of it all.
I suppose it could also be that all of the words aren't English words, which would make them pretty hard to say in English.