Thank you! I actually spoke to someone tonight in HK PwC. I have the answer now, so I figured I would post it for future questioners. It's not a good answer....
The 60 day trigger is cumulative and can be apportioned, BUT it only applies to business trips. These trips typically won't exceed a week at a time. If you have an assignment letter/contract, or the terms of your extended business trip are detailed out on paper, this rule doesn't apply. As soon as you are considered to be working in HK (on assignment, etc.), you are subject to filing. The HK return has a personal exemption of HKD 100,000 (about USD 12,850) for single folks. If you can get in and out of HK, on assignment, in under that amount, you will not have a tax liability. However, that HKD 100,000 has to include your salary, taxable benefits at home, per diem, hotel, completion bonus, dividends, etc. So, pretty much, you will have a liability.
In my case, if anyone is interested, because the lawyers have my visa paperwork (though not yet filed), and there is a signed document about me being on assignment, that is too far along in the process to change my assignment into a business trip. My boss is not going to be happy tomorrow....
