If it's easy to provide fog light ground locally suggest doing so. Then just hook up the blue/yellow to red wire each side.
To this end, no the blue/yellow wires are not permanently live they are controlled by the dash wiring which is already in place to an unused connector, allowing the optional fog light switch to be added. I may have mentioned this earlier. The actual electrics/electronics between switch and feed to lamps vary according to age of vehicle from direct feed to full BCU (software) control on those from around 2014 on. Note either before or after switch there will likely be built in control such that auxiliary lights are only powered with headlamps on to comply. The switch warning light will reflect this.
The inclusion of front fog light (blue/yellow) wiring within front part of chassis loom has been a feature of the Classics from at least 2006 and probably earlier. This is why I'm suggesting with a good degree of certainty they exist on your 2012 car. The wire colour codes are academic since MMC use same wires for long range spots or fogs. In any case the red/yellow colour code you mentioned is used for rear fog light wiring only. Even left and right headlamp wire colour codes are individual nowadays.
I agree that finding these redundant wires can be difficult with the monochrome effect courtesy of MMC spray on underseal but you definitely need to be looking with front wheels removed both sides. Look along base of inner wheel arch and remove a few cable ties if it helps.
Good luck.
