What is the deadline for collecting required number of signatures?

Referendum Act (amended date: 2018/01/03)

Article 12. For the matters prescribed in Paragraph Two of Article 2, the number of proposers shall be not less than 1.5% of the total electors in the most recent election of President and Vice President.

The list of joint signers of a proposal of referendum shall be submitted by the leading proposer to the competent authority within 6 months commencing from the day after receiving the model list of joint signers or an authentication code of the electronic joint signing system; if the leading proposer does not submit it within the aforesaid time limit, it will be regarded as abandonment of joint signature. [...]

Civil Servants Election And Recall Act (amended date: 2018/05/09)

Article 80. The period for collection of joint signatures referred to in Paragraph 2 of the preceding Article is as follows:

1. 60 days for recall of a member of the Legislative Yuan, municipal councilor, the governor of a municipality or the governor of a county (city).

2. 40 days for recall of a county (city) councilor, the chief of a township (city) or the chief of an indigenous district.

3. 20 days for a recall of a representative of a township (city) congress, a representative of an indigenous district congress, or the chief of a village (borough).

The calculation of the period referred to in the preceding Paragraph shall commence from the next day upon receiving the format of the list of joint signers.

The leading proposers of the recall shall submit an original and a copy of the list of joint signers all at a time to the election commission within the period prescribed in Paragraph 1; overdue submission will not be accepted.

The list of joint signers referred to in the preceding Paragraph shall be filled in column in the specified format in detail with the ID card numbers and addresses of domicile of joint signers, and bound into books by village (borough); where the list of joint signers is not submitted in the specified format, the election commission shall not accept it.

6 months for Citizens' Initiative; from 20 to 60 days for Recall Initiative, depending on the civil servant being recalled (see quotes from the law).