I am having the absolute hardest time finding a clear answer to this, so I decided to ask here.

My wife and I are planning on going to Asia next year. We're both citizens of the United States with valid passports. Our plan is to fly SFO-TPE-PVG-HKG-HND-LAX.

The only real important information here is that we are planning on entering Taipei for during our time there. We'll be arriving super early that morning, and our onward flight to Shanghai is later that evening, so it'll be a 14-hour layover. We would like to enter the city to get some food and do some sightseeing. Then we will be spending 3 days in Shanghai before traveling on to Hong Kong.

My question is this: Does this itinerary qualify for the 144 TWOV? I know, according to the rules, Taiwan and Hong Kong are both considered "third countries", but I cannot for the life of me find any information on what the rules are for when they are BOTH the bookend countries between our stay in Shanghai. I can't see a reason why it wouldn't work, but if anyone knows for sure one way or the other, I'd appreciate a direct answer to this.