Learn English – The origin of the term “Baker’s Dozen”

From The Encyclopedia of Word and Phrase Origins, by Robert Hendrickson:

The original version of this expression, 'on the water wagon' or 'water cart,' which isn't heard anymore, best explains the phrase. During the late 19th century, water carts drawn by horses wet down dusty roads in the summer. At the height of the Prohibition crusade in the 1890s men who vowed to stop drinking would say that they were thirsty indeed but would rather climb aboard the water cart to get a drink than break their pledges. From this sentiment came the expression 'I'm on the water cart,' I'm trying to stop drinking, which is first recorded in, of all places, Alice Caldwell Rice's Mrs. Wiggs of the Caggage Patch [1901], where the consumptive Mr. Dick says it to old Mrs. Wiggs. The more alliterative 'wagon' soon replaced cart in the expression and it was eventually shortened to 'on the wagon.' 'Fall off the (water) wagon' made its entry into the language almost immediately after its abstinent sister.

The idiom seems to be the opposite of keep one's shirt on. After a bit of Googling, I found the following reason which makes perfect sense to me:

So what does all this shirt business have to do with being annoyed? A Dictionary of Slang and Unconventional English by Eric Partridge suggests that it comes from the custom of taking off one’s shirt before fighting. I wouldn't argue with that.