Mars has a more eccentric orbit than Earth. Rather than flying in parallel imagine Mars on a diagonal path relative to Earth's orbit. The greatest brilliancy is based on a combination of Sun-to-Mars and Mars-to-Earth distance. Since Mars is moving away from the sun now, I would have expected greatest brilliancy to be just before the closest approach.
Actually the Greatest Brilliancy is the one I understand.
When Mars is at Opposition it is “Full”, that is 100% illumination. When it is at Closest Approach it’s not as full (Still 99%+), but that is enough that the slightly fuller phase will brighten it more than the growing distance away will dim it, so Mars at opposition will actually be brighter than closest approach.
It’s Greatest Brilliancy will be a combo of phase & distance but since phase changes generally have more of an effect than distance the Greatest Brilliancy will occur nearer to opposition vs closest approach.
Phase vs Distance works with the inner planets. Venus The farther it gets the fuller it becomes which pretty much means it’s always the same brightness no matter how close or far. An amazing coincidence, equal to that of the moon being the same size as the sun as seen from earth allowing total eclipses. Mercury on the other hand phase is everything which means it is always brightest during Superior Conjunction and will dim to Inf. Conjunction and vice versa.