Switching Visas between Jobs

I am resigning from a government job (MOEA) on Dec. 31 and starting a university post (MOE) on Feb 1. I plan to go to Hong Kong to get a visitor visa to get me to Feb 1., at which time I will convert to a resident visa. I am wondering…

  1. At the Consular office in Hong Kong, should I just say that I am going to Taiwan to visit? Or should I tell them what I am really doing? Does it matter?
  2. How long can I wait after Dec. 31 to go to Hong Kong for the visa? My current employer said there is no law (the old law said one can stay up to 14 days after leaving a job) but that I am probably safe up to 10 days or even 2 weeks.
  3. Is there any way I can avoid going to Hong Kong altogether? Could the Foreign Affairs Police just extend my stay – from Jan. 1 to Feb. 1 – if they have proof that I am, in fact, hired to begin a new post Feb. 1?

Does anyone have less-than-vague notions about any of this?

In order to answer your question(s), it would be necessary to have more information about your current status in Taiwan, especially: dates of issuance and expiry of your (a) passport, (b) ARC.

What is the “purpose of residency” on your ARC? Further details on your nationality, marital status, nationality of spouse, etc. would also be helpful for the purpose of analysis.