One of the major ways that both Hamlet and Things Fall Apart are timeless is the consideration of a hero that occurs in both of them. In Hamlet, the prince is a brilliant but indecisive young man tortured by the murder of his father and unable to do more than think hard about it for quite some time.
In Things Fall Apart, Okonkwo is a fierce and decisive man, never able to contemplate the consequences of his actions when he flies into a rage. He is tortured by the fact that his father was considered weak and had many debts and was completely useless in a fight.
So they appear to be on somewhat opposite ends of the spectrum, but they both end their lives in a tragic way, both acting as indicators of wrongs both done to them and with their societies and traditions. As heroes, they appear to be working in very different fashions but in the end they share remarkable similarities.
One other way in which both works might be considered timeless is the fact that they are both addressing cultural and traditional norms that are widely used in questioning both those areas. In Things Fall Apart it is the traditions of a native culture that seem completely absurd to outsiders and in Hamlet it is a religious world that dooms Hamlet's father to purgatory because he died "in his sins" while allowing his murderer to rise above that if only he dies after admitting his guilt and pleading for forgiveness.