"Here comes the Queen" versus "Here the Queen comes" [duplicate]

What's the correct one of the following sentences?

1. Here they come.

or

2. Here come they.

Consider for example:

3. Here comes the sun.

This is the title of a famous Beatles song.

Also consider:

4. Here the post office is.
5. Here is the post office.

Number (5) seems more natural than number (4). So which is better, or more natural, (1) or (2)— and why?

I'd think it'd be helpful to think of it as a matter of information packaging, rather than inversion, which is a somewhat artificial concept.

In English, the informational focus of a clause tends to come later. In other words, whatever information is central tends to come later.

Applying this principle to the OP's example 1 and 2, only 1 works because the focus is the verb come, not the subject they.

1. Here they come.

2. *Here come they.

Example 3 works because the focus is now not the verb comes but the subject the sun.

3. Here comes the sun.

Similarly, between 4 and 5, only 5 works because the focus is the subject the post office, not the verb is.

4. *Here the post office is.

5. Here is the post office.

As in @tchrist's example There but for the grace of God go I, context may determine what the focus is. As @Araucaria has explained it, I here is contrastive, which makes it the focus, not the verb go.

This contrastive focus is more frequently used in these examples:

A: I'm tired. B: So am I. (*So I am.)

A: I'm not tired. B: Neither am I. (*Neither I am.)

EDIT

While searching Subject-dependent inversion "here comes" on Google, among the first two results were the following EL&U and ELL questions, both questions answered but only the first OP accepted the top answer. See here

1. "Here he comes", "Here comes he" : The order of pronoun and verb in inversion
2. Why is it “Here you are!” but “Here comes the teacher.”?

Oh well, there goes my two hours...

ORIGINAL POST

1. a) Here eats the Queen

That doesn't work, does it? But if I move the subject to the front and place the adverb, here, at the end, it sounds better

1. b) The Queen eats here

Let's try a more formal announcement, a proclamation

2. a) Here arrives the Queen!

Nope, … still doesn't work. Although here is used to call our attention to something, to something of importance it still doesn't sound right with "arrival". There is no choice, we have to change arrive to come

2. b) Here comes Her Majesty
   c) Here comes the Queen!
3. d) Here comes the bride
   e) Here comes the sun
   f) Here comes trouble

The formula also works with longer sentences. For example, the children's rhyme Oranges and Lemons, first printed in 1744, has the ominous lines

3. g) Here comes a candle to light you to bed.
   Here comes a chopper to chop off your head.

Moreover, the iconic phrase “here comes the bride” was preceded by “Here comes the bridegroom” From Noël Antoine Pluche's The History of the Heavens, 1740

They all watched the time when the bride-groom was ready to go, and fetch his bride from her parents house, and to carry her to his own, with all the persons who were to attend and to be admitted into the banqueting room with him. So soon as he appeared, the two chorus's of young people taking their lamps, cried aloud: here is the feast, here comes the bridegroom. As they used to proclaim a funeral assembly, by putting some mournful ornament at the door of the deceased's house, and probably a dog with three heads to denote the three adieu's of his friends;…

Even today, the Boston Globe has as its title

4. Here comes Trump’s first State of the Union

Maybe this order only works with the verb, come?
No. It also works with the verb lie, which we often find in gravestone epitaphs:

5. Here lies John Doe

The expression "here lies" has its origin in Old English, and can be found in an Anglo-Saxon epic poem, celebrating the heroic Battle of Maldon in 991

Thought shall be the harder, the heart the keener, courage the greater, as our strength lessens.
Here lies our leader all cut down, the valiant man in the dust;
always may he mourn who now thinks to turn away from this warplay.
I am old, I will not go away, but I plan to lie down by the side of my lord, by the man so dearly loved.

I suggest that the formula Here comes and Here lies are among the vestiges of the English language that have survived to the present-day. Were we to use any other verb, e.g. eat, arrive, fight etc., the results will only sound peculiar to our modern English ears.

JK2 already posted a very good answer, please refer to it. I'm just adding my two cents here to expand on the topic, in case anyone is interested (it won't fit in a comment):

"Here they come" also implies an existing context--we've already been talking about "them" and know who "they" are. The focus of the sentence is the update on "their" actions/location. "Here comes [something]", on the other hand, implies that you're volunteering new information or pointing out a new subject that was not talked about previously. The focus of the sentence is the new subject. That's why it's somewhat unnatural to say "Here come they"--you would not normally use a pronoun to introduce a new subject of conversation, only as a stand-in for a noun already mentioned previously.

The same applies to the post office example:

We were talking about the post office, and look, here it is.

Look, here is the post office we were talking about.

Here comes the bride! Here comes the Queen! There goes the game! There goes my reputation! There goes my brother now! Here comes the son!

I would argue that these are essentially performative utterances using the deictic adverbs here and there as a pointing mechanism to underline the situation. They are only uttered in situ, as it were. Typically, here and there are used with the verbs come or go and are soldered to them for purposes of achieving the performative.

You can almost see the person uttering these sentences with his or her finger or hand pointing at them. They can also be characterized as being exclamatory utterances. In any event, there is no doubt they function performatively.

"Here comes the bride" is not at all like "The bride comes here". Ergo, I do not think one can talk of inversions here. Rather, they are special cases for pointing out a situation.

The usual usages are: Here comes x, Here goes x. There goes x. and are used in specific, real situations by speakers to emphasize the arrival or departure of a person, thing or idea. For an idea, such as "There goes my reputation", the sentence refers to an existing situation where something else is occurring and the speaker wants to underline this fact.

performatives in Mastering English: An Advanced Grammar for Non-native and Native Speakers