My impression from watching her interviewed: close friends called her Merman, not Ethel. After all, It was not her real last name. Mary Martin did visit her four or five times when Merman was diagnosed with an inoperable brain tumor. A lot considering Ethel lived in New York & Mary in California.
Always competitive, Merman finally used a walker after one of Mary's visits. And she kept using the walker, but it did not help much (unlike @Avalon).