The flavortext suggests that you need to look back at the cases (a double meaning word which refers to the murder mysteries in Round 1 and the containers in Round 2). Looking at each given phrase, you may notice that it includes references to one Round 1 puzzle answer and one Round 2 puzzle answer, in that order, placed at the very start/end of the phrase (indicated in bold below).
| Phrase | Round 1 puzzle/answer | Round 2 puzzle/answer |
|---|---|---|
| Female name blinks to separate blasts for familiar extraction | 1.7 The Dancer Who Showed Off Our Moves GIRL (female) |
2.6 Music Box ROLAND (name) |
| See quartet of strokes, characters in same places | 1.8 A Case Worth Re-examination WITNESS (see) |
2.7 Paper Container FOUR LINES (quartet of strokes) |
| Small animals, explosive, match hash and see red | 1.9 Woes of Our Pig Farmers LITTLE PIGS (small animals) |
2.3 Crate of Wood and Steel NITRO (explosive) |
| Take first third of colour in tree dish | 1.1 A Vibrant World CYPRESS (tree) |
2.1 Bento Lunchbox OMURICE (dish) |
| Same country, no steed | 1.3 The Art Workshop ZERO (no) |
2.9 War Chest BRONCO (steed) |
| Find origins of familiar names in clue order to poison motor | 1.2 Evidence Without Weight CYANIDE (poison) |
2.8 Toy Toolbox ENGINATOR (motor) |
| Repeated image keyword, unfamiliar skyscraper | 1.6 The Network Affair UNKNOWN (unfamiliar) |
2.5 Map Case THE CENTRIUM (skyscraper) |
| Celebration plan: see room from new angle | 1.5 Murder in the Lone Manor PARTY (celebration) |
2.2 Cardboard Package SCENARIO (plan) |
| Common solution loses back half in unceasing deconstruction | 1.4 The End of Iverson ENDLESS (unceasing) |
2.4 Jigsaw Carton UNSETTING (deconstruction) |
The rest of the phrase describes how to derive a word from each pair, based on some similarity that the paired puzzles share. The observant solvers might also have spotted some of these similarities (e.g. the vuvuzela blasts, the similar-looking pigpens and crate of wood & steel), which would help in the pairing of the puzzles.
...blinks to separate blasts for familiar extraction
The background blasts used in R1.7 The Dancer Who Showed Off Our Moves are vuvuzela blasts, also used in R2.6 Music Box. Separate the 80 vuvuzela blasts in the video, based on when the dancer blinks. (Note that the dancer doesn’t blink during close-ups.)
The blasts are separated as such: 4, 3, 17, 1, 9, 17, 12, 2, 8, 7.
The familiar extraction method to use is the one in Music Box: extracting from the performer’s name. The name corresponding to the vuvuzela is Fiepha Gnois-Mae Kerr. Extracting accordingly gives PERFORMING.
...characters in same places
Two similarly-shaped grids are used in R1.8 A Case Worth Re-examination and R2.7 Paper Container. Take the letters that appear in the same places in these grids to get ARTS (reading downwards).
...match hash and see red
Notice that the wooden sides and dots in R2.3 Crate of Wood and Steel both match the pigpen and fenceposts in R1.9 Woes of our Pig Farmers. In R1.9, the solution to the very first pigpen puzzle forms a hash symbol (#). Overlay that onto R2.3 by aligning the wooden sides of the R2.3 crate. If done correctly, the position of the dots will match exactly. “See red” suggests that you need to refer to the red pig in the R1.9 puzzle, which now lies over the ticket which says CENTRE.
Take first third of colour in...
The colour of the characters in R2.1 Bento Lunchbox is WITHERED ROSE, one of the Pantone colours that was used as a target in the fourth stage of R1.1 A Vibrant World. Take the first third of this, i.e. WITH.
Same country...
The same outline of the Singapore map is used in R1.3 The Art Workshop and R2.9 War Chest, depicting the country SINGAPORE.
Find origins of familiar names as clued by...
Some clues in R1.2 Evidence Without Weight contain names of the “Thomas the Tank Engine” trains in R2.8 Toy Toolbox. Both puzzles also use 8x8 grids (if you consider the R1.2 grid as 8 elements x 8 elements rather than 16x16 squares).
For each R1 name-containing clue, find the R2 box where that train track begins (‘origins’). Look back at the R1 grid and take the atomic symbol of the element in that grid position. In order of R1.2 clues (‘as clued by’), this gives the word FOUNDER.
| R1 name-containing clue | R2 box where train starts | Corresponding element |
|---|---|---|
| The Gift of the Magi writer _ Henry | Row 1, Column 7 | F |
| Gordon Brown from 2007-2010, for example | Row 1, Column 6 | O |
| Nintendo console for which Percy Jackson game was developed | Row 8, Column 1 | U |
| Initials of Harold Stanley's co-founder counterpart | Row 7, Column 1 | Nd |
| James Edward Smith's author abbreviation | Row 7, Column 8 | Er |
Repeated image keyword...
One of the statue images in first stage of R2.5 Map Case comes from R1.6 The Network Affair. The keyword as mentioned in R1.6 The Network Affair is STATUE.
...see room from new angle
A ball room appears in both R1.5 Murder in the Lone Manor and R2.2 Cardboard Package. The relevant extract in R2.2 Cardboard Package describes “standing in the centre [of the ball room] and staring at the east wall”. If you do this in the manor, you get this view:
The word to extract here is IN.
Common solution loses back half in...
FRONTLINE is the solution to the crossword clues in both R1.4 The End of Iverson and R2.4 Jigsaw Carton. Take away its back half to leave the word FRONT.
The complete cluephrase is PERFORMING ARTS CENTRE WITH SINGAPORE FOUNDER STATUE IN FRONT. This refers to the VICTORIA THEATRE AND VICTORIA CONCERT HALL, in front of which there is a statue of Stamford Raffles.