( וטעם וידום אהרן שהיה בוכה בקול ואז שתק או כטעם ואל תדום בת עינך (איכה ב יח)
The meaning of and Aaron was silent is that he had been crying was crying aloud before and then fell silent. Alternatively, it is similar in meaning to the verse "do not let the apple of your eye cease (Lamentations 2:18)", i.e., he ceased crying but did not necessarily stop making any sound at all.
(1) וידום אהרן, he consoled himself in the sanctification of the Divine name through which their deaths were made holy.
A Practical Guide to Rabbinic Counseling, Yisrael N. Levitis and Abraham Twerski (eds) at 173. "Following the funeral, the rabbi needs to assess the mourner's desire for solitude upon returning from the cemetery and the immediate days following, and respect his preference. Solitude gives the mourner space to think and get past many perceived obstacles to the problems of continuing life and experiencing the ugliness of death and its shocking finality. It is similarly important to respect the mourner's wish for silence. This is the reason why consolers traditionally need to wait for the mourner to speak first, thereby allowing him or her to set the agenda for their shiva call. Many mourners express their clear wish for everyone to "stay away." This should be honored. Silence gives mourners the space to reflect, feel what they need to feel, and collect themselves. Sometimes, silence speaks volumes. Just being with the mourner sans speaking banalities and trivialities is exactly the support the mourner needs.
Covenant and Conversation: Leviticus: The Book of Holiness, Rabbi Jonathan Sacks at 155. Jews are a people who have had more than their share of suffering. Like Aaron, they did not lose their humanity. They did not allow their sense of grief to be dulled, deadened, desensitized. But neither did they lose their capacity to continue, to carry on, to hope. Like Moses, they never lost faith in God. But like Aaron, they never allowed faith to anaesthetize their feelings, their human vulnerability. That, it seems to m, is what happened to the Jewish people after the Holocaust. There were, and are, no words to silence the grief or end the tears. We may say--as Moses said to Aaron--that the victims innocent, holy, they they died kiddush Hashem, "in sanctification of God's name." Surely that is true. Yet nonetheless, "Aaron remained silent." When all the explanations and consolations have been given, grief remains, unassuaged. We would not be human were it otherwise.
A Spirtuality of Listening: Living What We Hear, Keith R. Anderson at 131 "Listening stops when grieving begins. Adrenaline is pumped into the body and chemical reactions take place that create tears, fear, pain, panic and deep sadness. We all grieve in our own way. Some are silent while others wail in loud agony."
Moses as Political Leader, Aaron Wildavsky at 124. Aaron is the brother of Moses; Moses is told that he is to be as a god to Aaron, who is to learn from Moses as Moses learns from the Lord. The passivity that proved so pernicious in Aaron--for example, the Calf that virtually made itself--had been picked up from Moses. The Golden Calf is a consequence of purely passive leadership. The Calf is, therefore, a retrospective condemnation of Moses, embodying, as it were, the implications of his behavior from the burning bush to Mount Sinai: passivity becomes apostasy. When Moses prays for Aaron, he also asks forgiveness for himself--that is, for what he might have become had he remained at Aaron's level.