The only artist I can think of where I did this is Dr. Bombay.
A Swede/Dane pretending to be Indian doing a lot of crazy stuff.
What is probably his most well known song is Taxi, taxi, taxi! Where he sings about being a blind taxi driver in Calcutta, the music video was recorded in Malaysia:
Then there is this song about him taking over a relative's restaurant, notice the frogs os in the soundtrack....
Then he made this sexist song about how he want a wife who cleans, cooks and washes laundry for him, it is made with humor, so how serious it is I can't say:
There are more songs by this character, but the guy behind him then invented the same character to Dr. Mcadoo a crazy scotsman...
This time the songs where more focused on partying:
So a bit more generic...
Then he reinvented himself again into a carzy Mexican called Carlito.
I have not found any live action music videos by that character.
Here is his most well known song as far as I can tell:
I was wrong, there is one live action music video by Carlito:
Then he went away, only to resurrect Dr. Bombay a few years ago...
Dr. Bombay would never have got off the ground these days, the idea that a Swede/Dane could pretend to be Indian would just not be acceptable.
He still performes live and does ok from what I can tell, I am happy for him, but starting this kind of act these days would not work.