I've never managed to get to that island at night! I've found it a dozen times, but unfortunately only in the day.I like the summer shell island, that's when all the expensive bugs and fish come out. Best time to go is right after 5pm because you'll still be able to catch dorados along with sharks, arapaimas and arowanas + all the big bell beetles.
Get the good luck with belongings fortune from Katrina to lock in the seasonal islands and then approach Kapp'n right after 5pm. If he doesn't take you to the island you want, reset before auto-save kicks in and try again.I've never managed to get to that island at night! I've found it a dozen times, but unfortunately only in the day.