I am a UK citizen living in Taiwan on a JFRV, I do not have a company set up in Taiwan.
In my previous employment I was lucky enough to acquire some valuable skills related to the engineering industry.
Out of the blue, I have been contacted by a large company in Korea regarding the completion of some consultation-style work. It’s very short term but the pay will be considerable.
My problem is how can I get paid? I believe I must invoice the company in Korea for work performed and expenses. Will (can) companies pay individuals? Without a company, what are my options?
I think you’re thinking too much. You can issue a fa piao in Taiwan using just your personal tax number, but I don’t think you even need that for this. You’re an independent contractor, you can write up an invoice yourself, and if they send your money to Taiwan then you can report it to the tax people pretty informally – show them a copy of your contract with the company (if you had one), or a bank record, or indeed just write the numbers down with no supporting documentation (which is what I end up doing every year, since none of my income comes directly to Taiwan).
It’s possible that the Korean company needs something more formal, but that would be about their legal requirements, not yours, so you should ask them what they need.