Over the years, I have begrudgingly provided a similar service for a number of my employer’s associates. I don’t have a Chinese name for it; I refer to my end of the activity as “baby-sitting.” Mainland Chinese make up the bulk of visitors I deal with.
Generally speaking, I’ll do everything except book their flights. This broadly entails: Scooping 'em at the airport, arranging accommodation, planning their itinerary, accompanying them on their journey, getting loaded on their dime, and dumping 'em back at the airport after so many days. Many times they already know what they want to see; they just need someone to hold their hand on the way there (and back). However, one of the main attractions for the mainland consumer is having a surly foreigner in the pack. Rent-a-lǎowài.
Unfortunately, the business model itself is unstable and variable. Summer is high tide and you’ll have more bodies to manage than possible. More experienced travelers come in off-season, and hence, don’t need any assistance.
Those tour groups you see grinding through Taipei are called gànbù (幹部), and generally speaking, that’s how they’re used to rolling. I don’t think that’s what @finley is referring to, but it’s in the neighborhood. Foreigners as a rule don’t like to follow people around like Caesar’s dog pack. They fucking hate that. Just point them in a direction and say, “Meet me back here at 10.”
A number of people have approached me (directly or indirectly) about making this a viable business, and I can’t see it happening. On occasion, I have farmed out the tour guide aspect of the deal, and inevitably, the dude comes back and says, “I’m never doing that shit again.”
All that said, if you were to strike out independently, there are a bunch of back-end things that require your attention. First and foremost, you gotta know who is coming here, so that means doing a lot of research that starts with the MOFA and tourism bureau. Identify in which countries they’re promoting Taiwan. Denmark? Start poking around Danish concerns on Reddit and Facebook.
The act of managing a travel “agency” is time-consuming yet interesting in a way. However, the biggest issue is attracting clientele. It’s really hard. I don’t know what else to say about that.