Advice for Cycling around Taiwan

We did this:

Bike route 405311 - powered by Bikemap 

We learned this:

• Clockwise or anti-clockwise?: Plan your trip to take advantage of the prevailing winds.  The east coast of Taiwan is much  nicer than the west coast so plan to be riding into the wind on the east coast.  That way you will spend longer in the cleaner, mountainous, more beautiful parts of Taiwan of the east and less time cycling through the polluted air and flat landscapes of the west coast.
• If cycling on the east coast at Chinese New Year: Plan to be cycling against the flow of traffic to and from Taipei.  For much of the east coast there are few roads or even only one road that everyone must use to get farther north or farther south and these roads can get pretty busy and dangerous.  At the start of the Chinese New Year holiday all the traffic is heading south and you don't want to be sharing the only available lane south with a constant stream of vehicles including tour buses.  Vice-versa towards the end of the holiday.
• Police stations for cyclists:  Police stations have become bicycle stations in some parts of the country, particularly on the east coast.  There, you should find free water to fill your water bottles, toilets open to the public, and information, and you might find showers, tools, and rest areas designated for cyclists.  We didn't find any police stations offering campsites or space for sleeping in, but then, we didn't usually ask about it.  However, we did hear of one fire station on the east coast that was offering beds for NT$300 per night.
• Convenience store conveniences:  7-11s and Family Marts are also valuable resources for cyclists, sometimes offering public toilets and bicycle pumps for free use.  7-11 also has the i-cash debit card system which can save you from having to worry about hard currency.  It costs NT$100 to get an i-cash card and then you can add credit to it whenever you like and use it to pay for anything in the store.  I think Family Mart also has something similar.
• Traveling with your bike on the inter-city trains:  You can check the train schedule at the Taiwan Railways Administration website.  Enter your travel information and when the schedule appears you should see some trains listed with a bicycle icon.  These trains usually have a luggage carriage of some kind attached to the rear of the train in which you can leave your bicycle for the duration of the journey.  The ticket counter staff should allocate you a seat in the carriage closest to the luggage carriage.  However, the cost will vary depending on whether your bicycle is in a bike bag or not.  If your bike is in a bike bag then you can take it onto the train for free and leave it in the luggage carriage.  If you don't have a bike bag then you can still get the bike onto the train with you but you will have to pay for it.  You will also have to check it in at the shipping counter and it will be taken from you, put on the train, and then returned to you at your destination.  Note: this is only going to work on a train with the bicycle icon next to it on the schedule.
• Shipping your bike on the train:  Alternatively there are trains that travel around Taiwan for shipping stuff around the country and you can ship your bicycle on one of these trains.  It will be cheaper than paying to ship it on the same train as you (without a bike bag) but you will need to plan in advance: it takes a day or two for your goods to get to the destination on these trains.
• Traveling with your bike on the buses:  We have taken our bicycles on the inter-city buses although you should really have proper bicycle bags for this.  The staff at the bus stations seem very ambivalent and unimpressed when you turn up with your bicycle barely concealed within two large garbage bags that don't quite fit around it properly.
• Chinese characters for bicycle:

腳踏車 pronounced Jiăo tà chē

or

鐵馬 pronounced tiě mǎ (meaning iron horse)