Upvote:0
As you have a long layover and will probably leave the airport, therefore pass through immigration, you will need a visa. You can’t get a visa on arrival as Indians aren’t eligible for this.
Indians aren’t eligible for the e visa unless you travel with a group, but you can apply for the normal visitor visa here.
Upvote:3
United Airlines offers a web form to query TIMATIC, the database airlines use to determine whether or not they can allow you on your trip to minimize risks. While you didn’t share all of your details and I thus had to ballpark some of the required information, I did get the following reply concerning you, an Indian citizen with a passport not in immediate danger of expiring for transiting Taoyuan airport:
Taiwan - Transit Visa
Visa required.
Transiting without a visa is possible for:
Passengers transiting through Taoyuan (TPE) with a confirmed onward ticket for a flight to a third country within 24 hours. They must stay in the international transit area of the airport and have documents required for the next destination.
Important:
Passengers arriving after midnight must be escorted by the carrier to the transit hotel. Transit hotel is only available for Eva Airways (BR) and China Airlines (CI) passengers. If passengers wish to stay in the transit lounge, permission from the National Immigration Agency must be obtained. Before the passengers' arrival, the receiving carrier must be advised of the passengers' names, connecting flight number and destination.
(I removed the bits which concerned transit at Kaohsiung and the bits concerning former Chinese citizens.)
Thus, if you wish to remain in the international transit area of Taoyuan airport, that seems acceptable as your layover is less than 24 hours. If, however, you wish to exit the international transit area, e.g. to spend the night at a proper hotel, it seems you need a visa for Taiwan in advance.
I encourage you to redo this check using your exact data because it may or may not influence the results.