Very unsure about this one, but maybe my answer will spur someone to get it right. I'm hoping I wasn't completely off the mark.
The answer is:
The sun/solar eclipse
Always take care when you’re out,
For grace is not with you anymore.
Being outside can cause sunburn
Trains rely on the smallest things,
They keep everyone in community.
This one doesn't really fit, maybe it has to do with the chemical composition.
Many people will come together,
Bear witness to life’s greatest illusion.
The solar eclipse in a month will cause an illusion of nighttime during the day. People are travelling to see it.
The web spreads wider than most,
So cast a net for a gain in knowledge.
The eclipse is happening all across the U.S. for the first time in a long time. There is a big opportunity for viewing.
There is an author of this madness,
However it will not stop with him.
The moon? Maybe this means that it will keep moving.
The silver tongue may ramble on,
For it only shows you half truths.
Moon is deceiving us into believing it is night.
For that which is fundamental,
It becomes entirely perceptive.
The sun is fundamental, but it will 'disappear' for a little while.
The great heat that we all enjoy,
Is only a marker for something out of our control.
For the viewing of the eclipse, the sun only exists to mark the coming of darkness.
EDIT:
My answer was wrong, but I came back to take another look. Here are some thoughts:
Yet another to test the brain,
For they will come without end.
Always take care when you’re out,
For grace is not with you anymore.
Reads as some kind of 'evil' coming to get you. Could be referring to impure thoughts or temptation. Maybe it has to do with marriage? "Take care when you're out" because you don't want to cheat on your partner.
Trains rely on the smallest things,
They keep everyone in community.
Steam? Coal? Wood? These could make sense if you approach the sentence from a literal view. Coal would be most likely.
Many people will come together,
Bear witness to life’s greatest illusion.
Relates to the 'community' referenced in the previous paragraph. Life's greatest illusion is innocence, brother.
The web spreads wider than most,
So cast a net for a gain in knowledge.
op said this is supposed to be a command. The obvious message would be that "you probably don't know this answer, you will need to learn more by reading online".
There is an author of this madness,
However it will not stop with him.
The silver tongue may ramble on,
For it only shows you half truths.
These are also supposed to be commands, but I'm not sure what they're instructing you to do. They seem to be referring to a person who is spreading whatever evil or illusion the earlier paragraphs refer to.
For that which is fundamental,
It becomes entirely perceptive.
The great heat that we all enjoy,
Is only a marker for something out of our control.
I have only vague thoughts here. Words like "fundamental" and "great heat" give off a science-y vibe, but I can't really relate them. Second half could again be referencing something we enjoy but shouldn't.