I am physically based in Singapore while holding a stay pass (e.g. a Dependant’s Pass). Do I need a work pass if I am self-employed or working for an overseas-based employer?

You will need a work pass if you are in Singapore and are working for or providing services to a Singapore-based organisation (i.e. entity is registered with ACRA) or client. This includes all activities which are done for the purpose of gain. 

However, if you are in Singapore and are working for or providing services to an overseas-based organisation or client, you do not need a work pass.