He is a vice-chairman of the Kuomintang. In the 1990s, Lin was in the "non-mainstream faction" that aimed to be less confrontational with the People's Republic of China than Lee Teng-hui. He tried to replace Lee in the 1990 indirect presidential election, with Chiang Wei-kuo as his running mate.
He resigned his position as the head of the Judicial Yuan to become a presidential candidate in the 1996 elections. Since the Kuomintang did not nominate him, Lin ran as an independent. Though he originally considered Chen Li-an as his vice presidential running mate, finally he still picked former Premier Hau Pei-tsun, considering Hau's background might attract more mainlanders' votes for him. However because of his pro-China and pro-reunification standpoints during the Third Taiwan Strait Crisis, they only finished third with 14.9% of the vote. He has since retired from political affairs and secluded himself in Taichung after this defeat.
Lin is married to Chen Ho (陳閤) with one son and 3 daughters.