There is no clear path for a foreigner to get a credit card in Taiwan, unless you have a boat-load of money on deposit. All stories are anecdotal. I can’t speak for debit cards or deposit secured cards.
I have 3 credit cards now, and all 3 were obtained by knowing someone in a position to do something. Two of them are from banks that had previously rejected me, with a stable income history and a financially secure co-signer.
The first card I got was from First Bank. I was there one day getting travelers checks, the branch manager wanted to chat, when I was finished with my transaction he asked if he could help with anything else, I told him I was having trouble getting a credit card, and he took care of it. The second card I got was from Taipei Fubon, only because one of my clients used to work in their credit card department and was still friends with the manager. Both of those banks had previously rejected my applications. The 3rd card was from Standard Chartered, through an agreement with my employer for moving the business account there.