Tom Waits successfully sued Frito Lay for using an imitator without approval in a radio commercial.
The key seems to be that if someone is famous and their voice is distinctly attributeable to them, there is a case. In both of these cases, the artists in question were also solicited first and refused.
https://en.m.wikipedia.org/wiki/Midler_v._Ford_Motor_Co.
Bette Middler successfully sued Ford for impersonating her likeness in a commercial.
Then also:
https://casetext.com/case/waits-v-frito-lay-inc
Tom Waits successfully sued Frito Lay for using an imitator without approval in a radio commercial.
The key seems to be that if someone is famous and their voice is distinctly attributeable to them, there is a case. In both of these cases, the artists in question were also solicited first and refused.