Assuming you will take the high speed rail from Taoyuan station to Taichung station. In the early morning you "should" be ok with not booking tickets, it's possible but not likely that there will be zero seats left from Taoyuan to Taichung at 8am on 1/23. At the worst you may need to wait in line for a non-reserved seat, and/or stand for the 40-ish minutes it takes to get to Taichung. Coming back from Taichung to Taipei should be less of an issue although you could buy that ticket in the morning before you travel to Taichung, just to be sure.