I’m currently on vacation in Taiwan until July 8th
I don’t look like a foreigner since I am actually Taiwanese
Me & two other friends just wanted to sing & play our guitar at like Ximending or something
We aren’t bringing a mic or anything, just a guitar and maybe a chair lol
We aren’t asking for money, gonna put a sign that says
“No money please, just smile”
We just wanted to do it for fun
Will we be okay without the performance permit?
Or will we get in trouble…
All foreigners need work permits to perform publicly or even do volunteer work, unless the situation has changed recently.
Some years ago a foreigner hating over zealous cop busted a foreigner in Taidung. He was actually volunteering on a government event.
If it’s purely recreational and serves no economic purpose (for you or for anyone else), you have a clear argument for it not being “work”. However, the authorities might still say you’re not allowed to do it because you’re a tourist. 
More information:
Even if you clear up the work permit issue, you still need to conform with the laws about public order and so on.
The laws were changed a year or so ago regarding performers. Some info in visa or work threads I think.