My 0,02 € : don't rush your driving itinerary. I did a drive from Tainan over to Taitung a few months ago, and Highway 9 is not a fast drive as it is not an autoroute/freeway. Furthermore, there are sectors when crossing east/west between Feng-gang and Daren that are not fully improved, so it's a single carriageway that twists and curves through the mountains and you will inevitably end up behind a lorry. At night, not all vehicles are well illuminated (you'll see scooters or pickups without lighting) so prudence. Furthermore, there are contrôles automatiques (radars) so seeing as how you're from the US, speed limits will actually matter.

As a European, driving wasn't hard at all but it does take longer than what Google might suggest, and the infrastructure is not up to European standards.