According to this random post from 2015 I found by googling it, I was a candle , it was “only obtainable through Twitter interaction with Mr. Eaten or by stealing it from someone else who got one.”
According to the old wiki at Companions (Pets) - Echo Bazaar (wiki noted as “stopped being maintained in 2015”), it’s described as " Obtained as a gift from Mr Eaten.Very few known in existence, which can only be stolen in K&C."
So that about sums it up. It seems there wasn’t an in-game action to take to get it, just if the devs (probably Alexis Kennedy) noticed you interacting with the Mr Eaten twitter account in a way they/he thought was cool you’d get one; and you could steal one from somebody who had them in Knife and Candle.
Note that even in 2015, it was described as “certainly [hasn’t] been obtainable for a long, long time”, so they probably stopped being given out about 10 years ago.