the times to catch it in the northern hemisphere are July-November, 4am-8am and 5pm-7pm. the problem with the walking stick is that despite it only being like 600 bells, it's pretty uncommon and has a gimmick where if you walk too fast near it, it'll turn invisible (camouflaging with the tree).
you really have to go out of your way to find this guy bc it's unlikely you'll just come across it by accident since it's hard to see even when it isn't invisible. I think I've only ever seen like three of them
Visit my NL dream towns!
Angie from Maplerow, Ranae from Wayfield and Olive from Yorkwood
I'm with you on this one, I've been able to get rare bugs like the golden stag just fine, but GOD FORBID I ever find the walking stick. Seriously, I've only seen it once and of course it was when I wasn't actively trying to get bugs so I made it despawn
Don't talk to me or my 400+ sons ever again
And by "sons" I mean phones
I haven't had this experience, actually. I feel like I see them fairly frequently, and I caught at least a couple just today. The only advice I can give is simply to keep an eye out for them. They blend in pretty well, so they're easy to miss.
Update: I think they may be more common in the rain. It was raining in my town today and I caught five in the span of about fifteen minutes. That's definitely on the high end; there have been plenty of other evenings where it's rained and I haven't caught them at nearly so high a rate, but I think the fact that a lot of bugs aren't out in the rain at all makes the ones that are out more common.