For what it's worth:
Chocobo #1 (uncapped ISNM, Somewhat Warm egg) was raised in San d'Oria by 75 BLU:
Female. Foolishly alternated Take a Walk and Listen to Music care plans, fed Veg. Paste and a bit of everything else.
Result: No stats and no personality as of Day 20. Gave back to VCS for the crime of being yellow.
Chocobo #2 (Brutus quest, Bit Warm egg) being raised in San d'Oria by 75 BLU:
Male. Care plan Take a Walk only. Fed nothing but Vomp carrots.
Result: Developed Patient personality on Day 8, perky and still Patient as of Day 14.
Chocobo #3 (bought, Bit Warm egg) being raised in Windurst by 20 THF mule:
Male. Care plan Listen to Music only. Fed San d'Orian carrots and assorted greens.
Result: Developed Enigmatic personality on Day 9, stilll Enigmatic but now "a bit sick" on Day 11.
Chocobo #4 (bought, Bit Warm egg) being raised in San d'Oria by 01 MNK mule:
Female. Care plan Take a Walk only. Fed San d'Orian carrots and assorted greens.
Result: Perky, but still no personality as of Day 11. Fed it a Vomp to see if Patient will kick in.
Job notwithstanding, it seems to me the most influence you have on personality is choice of care plan, at least in the chick stage, with maybe a bit of boost from food. Of course, 4 chicks are a very small sample.
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