I don't know very much about people searching, but many here do. All I can think of is the phone call itself. Can you request the phone number for the month of the call, and then find it and call yourself? If it is a cellphone, and your father is 80, can you retrieve his phone and look up his older calls to the day your perhaps brother called?
Other than that, all I can think of is DNA on a database may find him. Input yours, and hope he has input his.
I do wish you luck, just a month or so ago, I was helped immensely in this forum with questions posed for my wifes' side of family.
Give them some time, the experts will arrive tomorrow