Wondered the same thing.
Looked all over etymolology sites and only the two you mention show up.
Here's what I found, just out of interest.
"close-fitting cap worn by women," from French cale "cap,"
the amnion enclosing the fetus before birth from 1540s. This, if the child is born draped in it, was supersititously supposed to protect against drowning (cauls were advertised for sale in British newspapers through World War I)