Let me clarify on the 4-month/6-month military conscription rule that's been causing a lot of confusion lately. I have dual citizenship (American and Taiwanese) and my brother went 90% of the way in applying for Taiwanese citizenship before backing out; I fall on the 4-month side of the rule while my brother falls on the 6-month side, so I'm pretty clear about the entire situation.
Pre-1985. If you're born BEFORE 1985, then you fall into the 4-month rule. Basically you cannot stay in Taiwan for more than 120 CONSECUTIVE days each time. Break this rule 3 times or stay in Taiwan for more than 365 consecutive days and you'll have to serve in the military. The obvious loophole to this rule is that you can board a flight to Hong Kong in the morning only to return in the afternoon, resetting your consecutive day count but still effectively staying in Taiwan every day of the year.
1985 and beyond. If you're born IN or AFTER 1985, then you fall into the 6-month rule. This is the new and current rule that replaced the 4-month rule because the government was wising up to everyone taking full advantage of the aforementioned loophole. Basically you cannot stay in Taiwan for more than a CUMULATIVE total of 183 days out of the year (January 1st to December 31st). Break this rule 2 times or stay in Taiwan for more than 365 consecutive days and you'll have to serve in the military.
The reason why my brother ended up not applying for Taiwanese citizenship was because he fell into the 6-month rule and there would be no point in having citizenship but not being able to live in Taiwan, so he decided to stick with the ARC. Fortunately, I am on the 4-month side of the rule and abuse this loophole to no end!
Of course, this only deals with military conscription AFTER you apply for citizenship. There are also rules regarding military conscription for the period of time from when you're 18 to when you apply for citizenship, something the government is going to look at if you want Taiwanese citizenship.
In a nutshell, all male Taiwanese citizens are required to serve a mandatory military conscription when they turn 18. The ONLY way to delay this conscription while living in Taiwan is education. As long as you are enrolled in high school, college, or graduate school, you can keep delaying the conscription. However, the minute you are no longer a student, conscription comes back to bite you in the ass. What does this mean for a prospective applicant? Let me explain.
Suppose you first came to Taiwan when you were 24 and have been working with an ARC ever since. Now, 6 years later, you're 30, and have decided to apply for Taiwanese citizenship. The government will look at the period of time from when you're 18 to 30 to decide whether you need to serve in the military. 18-23, you weren't in Taiwan, so no problem there. However, starting from when you were 24, you've been living in Taiwan. Now this goes back to which side of the 4-month/6-month rule you fall into. Suppose it's the 6-month rule. Well, since you've been living in Taiwan from the ages of 24-30, which is 6 years, you've clearly violated the 6-month rule, and will have to serve in the military IMMEDIATELY.
So before you decide to apply for Taiwanese citizenship, do the math and think about your time in Taiwan so far. A lot of people violate the 4-month/6-month rule without even knowing it, which isn't a problem if you're using an ARC, but will definitely be a pain if you ever decide to apply for citizenship. The way around this is to wait until you're 37 to apply for Taiwanese citizenship. The military only accepts men from the ages of 18-36. Once you're 37, you'll be free of mandatory conscription and the whole 4-month/6-month rule headache.
Oh, and of course, you MUST have an Overseas Chinese Stamp on your Taiwanese passport before you apply for Taiwanese citizenship, otherwise you'll have to immediately serve in the military regardless. The stamp can only be given by a Taiwanese embassy in your country of residence and NOT in Taiwan. So be sure to get this done before flying over.
Hope this helps!