Please be aware that Taipei has multiple airports and that these results are for all airports serving the city.
The best month to fly between Taipei and Manila is November and the most expensive month to fly is October. (Average prices, based on 558 datapoints.)
The best day to arrive at Taipei is Saturday and it would be best to avoid Friday, as prices are on average 45.9% higher than on Saturday. (Average prices, based on 525 datapoints.)
The best time to fly is at around 2. (Average prices, based on 1063 datapoints.)