You may know that keen means enthusiastic but why
as keen as mustard?
Mustard, and particularly Coleman's English mustard, is very spicy and in this sense keen is a synonym of hot.
It could also mean extreme in some way.
There was a bit of a
keen wind blowing through the valley.
So keen as mustard is a play on the double meaning of keen but for this idiom it means very enthusiastic.
Here's a classic, British advert with some aristocrats and a mustard crisis!