5th dnd – What can the artificer alchemical homunculus do outside of the fights?

This answer is based more on the interpretation than on the rules as they are written. The first thing to note is this:

The homunculus is friendly with you and your companions and obey your orders.

The second thing to note is this: the mental statistics of the alchemical homunculus are …

Int: 10 WIS: 10

For comparison purposes, these are the same mental statistics that a communist possesses. This means that your Homunculus is about as intelligent as a typical human being.

So, you have a tiny and flying construction that is about as smart as a typical human being and that obeys you to the best of one's abilities. This makes it significantly smarter than a familiar (the smarter has Int: 3).

So, yes, I would certainly say that it strongly supports the idea that your Homunculous can understand how you "signal". In fact, I said it strongly supported the idea that a Homunculus could be given and executed without problems. In terms of "difficulty", if a random player could understand how to do what your homunculus tries to do, he should also be able to understand it.