The "visa" that you refer to in your question is called Travel Authroization Certificate and is a sort of visa free entry applicable to citizens of India, Vietnam, the Philippines, Indonesia, Myanmar, Cambodia and Laos. As you have already said to obtain this free visa-free entry you need to meet the following criteria:
(1)The applicant’s passport must have remaining validity of at least six months starting from the date of arrival in Taiwan.
(2)The applicant must possess an onward/return air or ferry ticket.
(3)The applicant has never been employed as a blue-collar worker in Taiwan.
In addition, the applicant must possess at least one of the following documents issued by Australia, Canada, Japan, Korea, New Zealand, any of the Schengen countries, the United Kingdom, or the United States:
(1)Valid resident or permanent resident card
(2)Valid entry visa (may be electronic visa)
(3)Resident card or visa that has expired less than 10 years prior to the date of arrival in Taiwan
If you do not have these, you cannot make use of this visa-free entry and must apply for a regular visa at the Taiwan embassy. The website about visitor visas to Taiwan is here. For Indian nationals I found this unofficial link, which lists the documents required and fees that has to be paid for a visitor visa. Some overview of requirements for a tourist visa (from the same site):
The Applicant should have a passport valid for at least 6 months from the date of application.
Photocopy of the applicant's passport.
One Visa Form (The Applicants need to fill online visa form at the website https://visawebapp.boca.gov.tw and take the printout of filled online form, should be signed by the Applicant).
Two recent passport-size photographs (35 x 45 mm) against a white background.
Confirmed onward/ return air ticket.
Visa Request Letter from Travel Agency in India or Taiwan with detailed itinerary and payment proof or Invitation letter from Taiwan's inviter.
A Covering Letter from the Company or the Applicant mentioning the purpose of the visit and the duration of stay (in original).
Personal financial proof (Form 16 for 3 years, ITR for 3 years or Original personal bank statement for 3 months with bank seal on each page with signatures of Bank's Authorising Signatory) Kotak Bank payment slip of the visa fee.
Hotel confirmation required, for the period of stay.
Visa is valid for 3 months with a maximum stay of 60 days from the date of entry.
Processing time is 3 working days for Normal case and next day collection for Urgent case.
The visa fees varies from Rs. 3,300/- (Single entry) to Rs. 6,600/- (Multiple entry)
You can also visit the official website of embassy in India although it is not very clear. Maybe you can send them a mail for more information such as the exact mechanism of visa fee payment.
They have a link about tourism visa that was updated in 2014, which should get you started.