Did you brother get Household Registration (ROC ID) ever in his life before? If not, then don’t apply for an Overseas Chinese ID. You can enter/exit Taiwan on a foreign passport without conscription problems. You can also work in Taiwan without conscription issues. Just apply for an ARC using your foreign passport.
If your brother has had Household Registration (and thus an ROC ID number), then he should apply for an Overseas Chinese ID (if he is eligible). He will not have to serve if he doesn’t stay in Taiwan for more than 183 days in a calendar year or 365 days continuously. If he wants to work (and stay longer than 183 days) in Taiwan during ages 19-36, the only way to avoid conscription is renouncing his ROC Nationality/Citizenship. Renouncing nationality/citizenship without fulfilling conscription is only eligible for Overseas Chinese (or anyone under 15 years of age).