In what circumstances, if any, is it advisable to file 1040-X before the original return is processed?

Some sources suggest "never":

You must wait until the IRS has processed your tax return before making corrections.

Or suggest "never if your original return claimed a refund":

If you’re due a refund on your original return, wait until you actually receive the refund before filing an amended return for that tax year.

But it seems the answer isn’t "never", because the IRS states:

If the amended current year return indicates the taxpayer owes money, file Form 1040-X and instruct the taxpayer to pay the amount by the April due date to avoid interest and penalties.

The IRS also states:

Taxpayers filing an amended return because they owe more tax should file Form 1040-X and pay the tax as soon as possible. This will limit interest and penalty charges.

Confusingly, this question seems to indicate that amending immediately — "had some income I’d forgotten about and wanted to right the situation as quickly as possible" — led to trouble!

But going by the IRS statements, if a taxpayer files and pays say in early April and then quickly notices a mistake that means more tax is owed, they should file 1040-X with an additional payment by April 15 even though the original return has not been processed by then, right? And likewise, even if the mistake is noticed after the due date (but before the original return is processed), amending ASAP is recommended to reduce the penalties?

Does this also apply if the original return indicates a refund, but the amended return reduces the refund? If 1040-X is not filed immediately, could penalties apply when the taxpayer waits for the the IRS to provide the original (too large) refund before amending? One source urges waiting, but without explaining whether this could increase penalties:

wait until you’ve already received your refund before you mail in your amendment with payment.

Shouldn’t 1040-X be filed immediately to reduce the risk of over-refund (i.e., the IRS penalizing you for the time during which you have money that isn’t rightly yours)? However, this could be read to contradict another IRS statement:

If the amended return indicates the taxpayer is due a refund, be sure to advise that:

• Before mailing the amended return, the taxpayer must wait until the original return is processed.

There is a potential ambiguity in "the amended return indicates the taxpayer is due a refund" — does this mean a refund in absolute terms (less tax owed than payments made), or a refund relative to the original return (less tax owed than stated originally)?

Now, what about the case where more tax is not owed? The one case that seems very clear is that if the amended return is claiming an additional refund (relative in the above sense), then the taxpayer should wait until the original return is processed:

If you are filing to claim an additional refund, wait until you have received your original refund before filing Form 1040X. You may cash that check while waiting for any additional refund.

But what about a case where the original return shows a refund, and an amended return is necessary but makes zero change to this refund? An example is fixing an omitted capital gain item, when the net result remains a capital loss capped at $3,000. The amendment doesn’t affect the current-year tax owed, but reduces a too-large loss carryover and thus causes a potential increase in tax owed in future years. In a broad sense, it can be viewed as correcting an understatement of income.

A taxpayer — as in the question linked above — might think that an inadvertent understatement of income of any kind, once discovered by the taxpayer, should be corrected ASAP to show good faith, rather than waiting for the IRS to catch it. Yet, the opposite has been suggested:

The upside is that if the IRS catches the mistake first and you receive a letter or a notice about it, it may not be necessary to prepare an amended return…

It seems odd to call it an "upside" since it makes the taxpayer look less-than-conscientious. Isn’t it be better for the taxpayer to fix it on their own initiative and thereby help show, if there were any doubt, that they weren’t trying to "get away" with anything?

Is there any validity to this thinking, and is immediately filing 1040-X (before processing of the original return) ever a good step? Or, if the rules say 1040-X should not be filed until later, is there another useful way to demonstrate good faith? For example, should the taxpayer immediately send a plain letter to the IRS noting the discrepancy and the intent to file an amended return at the appropriate time?

EDIT: It’s been suggested that if more tax is owed, payment can be made immediately without 1040-X. This seems to be supported here:

If paying a 2019 income tax liability without an accompanying 2019 tax return, taxpayers paying by check, money order or cashier’s check should include Form 1040-V, Payment Voucher with the payment.

But in the scenario discussed where a mistake (inadvertent understatement of income) needs to be corrected but does not result in current additional tax owed, what about the question: "is there another useful way to demonstrate good faith? For example, should the taxpayer immediately send a plain letter to the IRS noting the discrepancy and the intent to file an amended return at the appropriate time?"