Taichung is a city in Country.
South towards Tainan
You can catch the train to Chenggong Station (成功車站), then take either exit and make your way to any of the entrances to Highway 1 （See below for one specific option).
Note, there's a Hi-Life (like a 7-Eleven) just to the south of Chenggong Station (成功車站) at which you can stock up. One hitcher got cardboard (zh3xiang1, 紙箱) and borrowed a pen from there to make a sign.
You can take the south exit from Chenggong station and follow the path detailed below to a decent hitching spot at one of the entrances to Highway 1.
It's safer than it looks. Most cars are going pretty slow (approx. 50-60km/h) and have plenty of time to pull over in the space that's available (see image below).
Ollie waited here (see image above) for 3 minutes before getting a lift to the outskirts of Tainan, where he got another lift after 2 minutes right into the city centre. The exact place where he stood was on the raised section in between the lanes.
South East towards Pingtung on Expressway 3
Sven got picked up in a few minutes at this spot on a direct ride to Kaohsiung. The cars are pretty slow and have a lot of space to stop right after the traffic light. You'll catch all the traffic going south to Expressway 3 and two bus stops are close by to get there easily. In general, drivers kept recommending to have a sign and that they don't pick up people without one.