Hi,
I don't think that we have the same 3x great grandfather but we could have a futher back great gf. My Great grandfather was Edward Callaghan, I have to double check but he was born c1871/2 and I think his father's name was Michael. There is always a chance that your Thomas was related to that Michael closely. In a few weeks I plan on going into the GRO in dublin, the geneology office, and having a look. I'll see what I can find. I know that Edward Callaghan had a son Thomas (my great uncle) and maybe it was a family name. If not then at least we'll both know, and I'll have a look for Thomas Callaghan while I'm there, Just in case, but it won't be for a few weeks yet.