I am in August month right now and according to guide it is the easiest month to catch banded dragonfly but I been TT-ing in the day time and all I can get is darner only! Is the weather a problem? Cause I read somewhere is available in rain but I have TT 12 days in August but apparently summer is so sunny!!
You can get banded dragonflies on some of the tours - not the bug ones as you can't keep the bugs; but some of the others allow you to get a net from Loid - try the easy balloon (you don't want pitfalls), any of the hide seek, possibly the gardening ones.
I've certainly caught them on the easy balloon.
I tend to find them near water, ponds or along the river. There's no guarantee you will find them on a tour.
(an aside:Fairly certain I've never caught a giant petaltail on a tour (apart from bug tours where you catch them for medals). Had to get those in my town).
Dragonflies don't appear on the island, just some of the tours.
I caught one on the tours and the only tours I have ever done are the hide and seek and the one I can't remember the name of where you have to collect furniture from a list. It's been so long since I did any tours at all
But I would definitely try that, good luck!