Sorry Mr. Masala, I missed the coming into effect of the aforementioned provisions of the Act for the Recruitment & Employment of Foreign Professionals because I foolishly expected the Labor Pension Act to be amended. Instead they’ve left the LPA exactly as it was, so you can’t understand the LPA by reading the LPA (because the AREFP rewrites part of it), just as you can’t understand the LSA by reading the LSA (because the LPA rewrites part of it). 
What @Alex1000 quoted earlier in this thread matches the English text of Art. 11 at Act for the Recruitment and Employment of Foreign Professionals - Article Content - Laws & Regulations Database of The Republic of China (Taiwan) except that the version which was passed has one more paragraph at the end:
The provisions of the preceding five paragraphs shall not apply to foreign professionals as referred to in the first paragraph who were already covered by the Labor Pension Act prior to the enforcement of this Act.
That just prevents foreign spouses from having their pensions reset.
However, there’s still room for more confusion! 
Foreign professionals who are hired to engage in professional work, and who have been approved for permanent residence by the National Immigration Agency, Ministry of the Interior, shall from the date of enforcement of this Act be included in the retirement pension system under the Labor Pension Act.
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Are they saying a foreigner who obtains PR status due to five years of “professional work” qualifies for the new system, but a foreigner who obtains PR status due to five years of marriage doesn’t? Is it just your ARC status at the time you become a PR that matters? What if you’re working but on a marriage-based ARC?
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“Professional work” in this context means “white collar” work i.e. jobs covered by Art. 46 Par. 1 Subpar. 1 to 6 of the Employment Service Act. As much as some legislators hate this concept, it is possible for a human being to have both blue and white collar jobs in a single lifetime.
So, is it only the color of your collar at the time you become a PR that matters? Or do you lose your pension if you spend a day hauling bricks, doing household chores, or caring for an elderly relative? 
Anyway, if you are a PR and unambiguously employed as a “foreign professional”, whether normal, special, or senior, provided that you don’t request not to be switched over to the new system, you should automatically be switched over.
According to the MOJ’s record of the AREFP, which for some reason seems not to have been available until June 8th, 2018 (“last updated” on that date even though there’s been no amendment since promulgation), the Act came into effect on February 8th, 2018.
1.中華民國一百零六年十一月二十二日總統華總一義字第 10600140481 號令制定公布全文 22 條；施行日期，由行政院定之中華民國一百零七年一月二十九日行政院院臺教字第 1070002554 號令發布定自一百零七年二月八日施行
If I’m reading Art. 11 Par. 5 correctly, your employer has until 6 months and 15 days after that date – so late August – to register you for the new system at the BLI.
Your seniority starts from when the date you started your current job, not from the date of the switch.
For teachers who are also PR’s:
“Authorized manning strength”! 
Here’s the original: 受聘僱擔任我國公立學校現職編制內專任合格有給之教師…
I’m not sure about that, but since I get a headache trying to keep track of the rules for the different kinds of non-buxiban teachers, I think I’ll leave it to @tando to figure this one out.