Hello everybody, I've been digging around to understand exactly how the timing of miracle is working but am having a little bit of trouble despite looking at the comprehensive rules. Below are the relevant rules I have found and how they are working with miracle, and I would like to clarify my understand of them in regards to the following situation:

You have drawn no cards during your opponent's turn and you cast Brainstorm, with the first of the three cards drawn being a Terminus.

Since Terminus has is a miracle card, we need the miracle rules,

Quote Originally Posted by MTG Comprehensive Rules
702.92a Miracle is a static ability linked to a triggered ability (see rule 603.10). "Miracle [cost]" means "You may reveal this card from your hand as you draw it if it's the first card you've drawn this turn. When you reveal this card this way, you may cast it by paying [cost] rather than its mana cost."

702.92b If a player chooses to reveal a card using its miracle ability, he or she plays with that card revealed until that card leaves his or her hand, that ability resolves, or that ability otherwise leaves the stack.
For complete understanding of linked abilities, here is the relevant linked ability section,

603.10. Some objects have a static ability that's linked to a triggered ability. (See rule 607, "Linked Abilities.") These objects combine both abilities into one paragraph, with the static ability first, followed by the triggered ability. A very few objects have triggered abilities which are written with the trigger condition in the middle of the ability, rather than at the beginning.
So rule 603.10 tells us that the Terminus has the static ability "You may reveal this card from your hand as you draw it if it's the first card you've drawn this turn," as you can do this whenever the condition is true. Then there is a linked trigger ability, "When you reveal this card this way, you may cast it by paying [cost] rather than its mana cost."

Okay, with that in mind let's say you cast brainstorm. We know that during the resolution the Miracle ability will trigger if you reveal Terminus. For this triggered abilities happening during the resolution of a spell or ability I found the following relevant rules,

603.2. Whenever a game event or game state matches a triggered ability's trigger event, that ability automatically triggers. The ability doesn't do anything at this point.

603.3. Once an ability has triggered, its controller puts it on the stack as an object that's not a card the next time a player would receive priority. See rule 116, "Timing and Priority." The ability becomes the topmost object on the stack. It has the text of the ability that created it, and no other characteristics. It remains on the stack until it's countered, it resolves, a rule causes it to be removed from the stack, or an effect moves it elsewhere.
So during the resolution of brainstorm you draw one card. This is the first card you’ve drawn this turn, so Terminus’s static ability comes into play, allowing you reveal it from your hand. Then the second clause on terminus is triggered. However, from rule 603, this trigger just happens but since we’re currently in the resolution of brainstorm no play has priority, so this trigger cannot be put on the stack yet. Terminus remains revealed as you draw your second, and third cards.

Next, if neither of the two cards you put back on top of your library for the brainstorm are the currently revealed Terminus, you may put Terminus’s triggered ability onto the stack.

On the other hand, if one of the cards put back was terminus, I am a bit confused. Terminus has left your hand, so per the Miracle rule 702.92b it is no longer revealed. However, the trigger condition for Terminus was still met since it was revealed. So, does any trigger go on this stack for this? I can’t find a rule that would prevent the Terminus trigger from going on the stack. The trigger only happens on the reveal of Terminus, and the triggered condition of Miracle doesn't say that the card itself needs to be currently revealed for the ability to trigger.

So, if this trigger goes on the stack still, why are you no longer able to cast the Terminus sitting on top of your library? I would guess that the Terminus becomes some "new object" when it becomes unrevealed by going on top of your library, although I could not find a rule to say this. In fact, if there is no rule saying that the Terminus on your library becomes a new object, then the below rule relating to the revealing of cards may contradict the miracle rule about the reveal,

701.13a To reveal a card, show that card to all players for a brief time. If an effect causes a card to be revealed, it remains revealed for as long as necessary to complete the parts of the effect that card is relevant to. If the cost to cast a spell or activate an ability includes revealing a card, the card remains revealed from the time the spell or ability is announced until it the time it leaves the stack.
Since miracle rule 702.92b says the card is unrevealed when leaving the hand, but if a triggered ability still goes on the stack rule 701.13a and there is nothing stopping it from being cast, it makes me think that Terminus needs to remain revealed, even in your library, so that you to have an opportunity to cast it. That said, it seems silly to me to cast a Terminus from your library, but I just can't find the rule which prevents this from happening. So there has to be some rule either preventing the original trigger from going on the stack, or from separating the connection between the Terminus on top of your library from the same card which made the triggered ability in the first place.

I don't think it has to do with the fact that you can't cast Terminus from your library, since the below rule does not specify the spell has to come from the hand, but merely suggests that's where spells are usually cast from. Additionally, the Miracle rules themselves don't specify that the card has to be cast from your hand either.

601.2. To cast a spell is to take it from where it is (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect.
Dealing with what happens during the resolution of the miracle trigger is pretty quickly described with the following rule,

608.2f If an effect gives a player the option to pay mana, he or she may activate mana abilities before taking that action. If an effect specifically instructs or allows a player to cast a spell during resolution, he or she does so by putting that spell on top of the stack, then continuing to cast it by following the steps in rules 601.2a-h, except no player receives priority after it's cast. The currently resolving spell or ability then continues to resolve, which may include casting other spells this way. No other spells can normally be cast and no other abilities can normally be activated during resolution.
So, per this rule, while the miracle trigger is resolving you may choose to cast the Terminus by following all the steps for casting a spell. Only after Terminus is put on the stack or you choose not to cast it has the miracle trigger finished resolving.

Anyway, I know this is very technical, but I'd appreciate some help in clarifying where my understanding of these interactions is going wrong. Thanks in advance.