This trail ('Gate 1') is located off Highway 14A, very close to the 16km marker (not 15km as is reported elsewhere). The actual gate or gateposts are not visible from the main road, but the entrance can be identified by a sign for 'Rueiyan River Major Wildlife Habitat' and a number of water pipes that run along it.
There's parking on the right a short distance up the main road. The trail has recently been cleared making it much more accessible. After about 5km the trail crosses a small road (about half a kilometre down from from the police station where's there some excellent mothing) and then continues – passing an actual blue gate, 'Gate 2' – for a further 12km where it ends at the head of a valley. Thus visitors can walk for up to 17km if they've the energy, though sometimes the road is damaged by typhoons.
This is the area referred to as the continuation trail. Pheasants can be seen here, as well as other high-altitude endemics such as the Taiwan Hill Partridge. This trail can be very wet due to leaking pipes, so it's best to wear rubber boots or carry spare footwear. During the dry season you'll do OK gingerly edging along the less-wet parts.
The Taiwan Forestry Bureau has published a good leaflet about the area. It is, alas, very difficult to obtain. Guided tours of this trail can be organised by Taiwan Eco-Tours.