Harry's claim: How hard is it to deliberately cause a Priori Incantatem?

Question

In Deathly hallows, Harry fears that by using Priori Incantatem, the Death Eaters could work out that his wand was broken:

“Priori Incantatem,” said Harry. “We left your wand and the blackthorn wand at the Malfoys’, Hermione. If they examine them properly, make them re-create the spells they’ve cast lately, they’ll see that yours broke mine, they’ll see that you tried and failed to mend it, and they’ll realize that I’ve been using the blackthorn one ever since.”

_{Deathly Hallows, Chapter 24 - The Wandmaker}

Almost everything I know about this phenomenon is through Dumbledore's explanation in Goblet of Fire:

“The Reverse Spell effect?” said Sirius sharply.
“Exactly,” said Dumbledore. “Harry’s wand and Voldemort’s wand share cores. Each of them contains a feather from the tail of the same phoenix. This phoenix, in fact,” he added, and he pointed at the scarlet-and-gold bird, perching peacefully on Harry’s knee.

...

“So what happens when a wand meets its brother?” said Sirius.
“They will not work properly against each other,” said Dumbledore. “If, however, the owners of the wands force the wands to do battle . . . a very rare effect will take place. One of the wands will force the other to regurgitate spells it has performed — in reverse. The most recent first . . . and then those which preceded it. . . .”

_{Goblet Of Fire, Chapter 36 - The Parting of the Ways}

So we know that the effect requires that both wands share cores (from the same animal, not just species; this answer shows what they could be). This will cause them to not work properly against each other and connect. The regurgitation starts after one owner has won the battle. However, I find it hard to comprehend how the Malfoys could find the right counterpart to Hermione's wand in the first place. Oh, and Dumbledore calls this a very rare effect.

• Is the effect easily re-creatable?
• Also, does another occurrence of this effect exist in-universe? If yes, perhaps it would come in handy.

Answer 1

As @ChrisHayes comments, you wrongly assume that the Piori Incantatem only happens when two twin/brother wands duel against each other.

A great example is the excerpt where the Priori Incantatem is firstly introduced (emphasis mine):

‘Well, we’ll soon see,’ growled Mr Diggory, looking unimpressed. ‘There’s a simple way of discovering the last spell a wand performed, elf, did you know that?’

Winky trembled and shook her head frantically, her ears flapping, as Mr Diggory raised his own wand again, and placed it tip to tip with Harry’s.

‘Prior Incantato!’ roared Mr Diggory.

Harry heard Hermione gasp, horrified, as a gigantic serpent-tongued skull erupted from the point where the two wands met, but it was a mere shadow of the green skull high above them, it looked as though it was made of thick grey smoke: the ghost of a spell.

_{Harry Potter and the Goblet of Fire, Chapter 9: The Dark Mark.}

It's true, however, that the explicit Prior Intantato spell is much weaker than the "natural manifestation"¹ of the spell, as the conjurer's wand forces the target wand to regurgitate but one spell, contrarily to effect Dumbledore describes:

One of the wands will force the other to regurgitate spells it has performed — in reverse. The most recent first . . . and then those which preceded it. . . .”

_{Harry Potter and the Goblet of Fire, Chapter 36: The Parting of Ways.}

Apparently, Prior Incantato can be used iteratively to recreate the most recent spells one by one, ultimately achieving the same effect of a natural Priori Intancatem (emphasis mine):

‘But he’ll know soon, if he doesn’t already, that mine’s broken beyond repair,’ said Harry quietly.

‘No!’ said Hermione, sounding frightened.

‘He can’t know that, Harry, how could he –?’ ‘Priori Incantatem,’ said Harry. ‘We left your wand and the blackthorn wand at the Malfoys’, Hermione. If they examine them properly, make them recreate the spells they’ve cast lately, they’ll see that yours broke mine, they’ll see that you tried and failed to mend it, and they’ll realise that I’ve been using the blackthorn one ever since.’

_{Harry Potter and the Deathly Hallows, Chapter 24: The Wandmaker.}

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_{1: One could theorise that the Prior Incantato was invented to mimic the effect of this natural, powerful magic, and the effect was named after the invented/discovered spell (and not the other way round). You can read more about the process of inventing spells here.}