I’ve searched briefly, but forgive me if this question has been answered b4.
I would like to perform as a musician on a regular basis at various venues around Taipei.
My wife is Taiwanese and we have children. I still hold a 3yr ARC and one of those open-work permits.
My question is, Am I putting myself in jepordy and legal limbo land.
Respect
Is your ARC based on a JFRV (Joining Family Residence Visa) or is it work-based? If its the former, you don’t need a work permit at all, open or otherwise.
As for the legality of performing with a JFRV, I think you’ll be OK. I do it all the time.
There’s a chance you could get busted, as I believe it’s illegal for anyone to perform anywhere for money without a permit. However, the punishment would be the same as for a local – some kind of ticket and a fine – although I’ve never heard of anyone getting busted this way.
Thanks for the relief 
I’ve got a friend who goes busking most nights, and she’s been busted by the cops a couple of times. Generally they don’t care - as long as you’re not being disruptive or causing anyone any trouble, they’ll leave you alone, and if they do pull you up on your performing, as long as you’re polite and respectful they’ll generally just let you off with a warning.