I also tend to get ...intrigued by sayings. I always have an urge to find out where they are from and why. In this case its easy to see what it is saying, but harder to understand fully why it is.
Squirrels (as everyone knows) eat nuts. They store them in various ways to get them through the winter. Most people only know them as storing nuts in a 'larder' which they eat in winter. What is less known is that squirrels also bury nuts, and mark the location for later unearthing and eating. However, and industrious squirrel stores many more nuts than most people think, burrying a lot of them. Squirrels have only small brains, and so it is inevitably true that a lot of the burried nuts do not get eaten for various reasons (cant remember where to dig, ground frozen, etc etc). So the phrase to 'squirrel' things away, means to put the item(s) in various places, NOT all of which will be remembered or retrieved. Its meaning changed over time to mean to put something away (usually in a hidden/secure area).
A complete digression from anything useful I know. But what the hell!