Hong Kong to Taipei via Shenzhen

Unfortunately, this is not possible because 24 hour visa free transit does not allow the possibility of entering Guangdong province from Hong Kong by bus or train and then to reconnecting to a flight out of China. This is doable only under 144 hour visa free transit, but only by ferry from Hong Kong to Shekou or Nansha ports and only to the citizens of 54 countries are eligible for this scheme. It is also possible to to apply for Shenzhen 5 days visa on arrival at Lo Wu / Luohu border crossing, enter Shenzhen and then depart from Shenzhen to Taiwan by a direct flight. Indian citizens are eligible for Shenzhen 5 days visa, but the success rate is not exactly the best. Your chances would be good since you will be able to present your flight ticket out of Shenzhen to a third region, but it is so hard to recommend you something that is of doubtful success.