The correct term is idioglossia, which my brother and I never engaged in.
Though we have a couple of times posted on FR almost verbatim posts on the same thread within seconds of each other with 2,200 miles between us
My grandfather is an identical twin. Because of WWII, he and his brother were never really home at the same time for a few years. Well, on of their nephews, who was only 3 or 4 years old at the time, had never seen them together. They had leave at the same time and went to their sister’s house. The nephew saw them together and freaked out! LMAO He ran into the yard and wouldn’t come in until his dad told him what was going on.