If SWIM was living here for 3 years and then got married, would they be eligible for naturalization based on having 3 years residency up until that point and being married to a Taiwan citizen? What if they changed their employment-based ARC to a marriage based ARC?
It doesn’t. Actually, it doesn’t depend on your ethnicity, nationality or gender at all.
TL;DR I don’t know, but if someone tells you no, try pushing back.
Nationality Act Article 3 and 4 and the Enforcement Rules of the Nationality Act are the relevant laws.
They don’t shed much light on the role the “purpose of residence” plays in the application.
Based on recent experience, I think the interpretation of this rule is something that could be one of those things that possibly vary from Household Registration Office to Household Registration Office. The HRO has access to some systems related to calculating your residence duration (others who have applied did not need to provide a Record of Entry and Exits, for instance), which one would assume show the purpose of residence. They need that to exclude the time you were a blue collar worker or a student etc. It might be an area HRO staff make independent choices based on the lack of definition.
That’s for getting the paperwork accepted for submission. Then, since the HRO’s job is to send the paperwork deeper into the Ministry of Interior there could be a further different interpretation and it could be accepted or denied there.
There have been a lot of different comments on this forum about switching between ARC types and between ARC and APRC causing problems with naturalization applications. However, I can’t find any concrete justification for this, aside from the switch causing gaps in the residence period or an accidental change in ID numbers. The only one I’ve chased down to confirm there is no issue: Employment ARC to Gold Card.
A less than useful response, I know 
Personally, I would like to think SWIM could get naturalised as soon as possible.