This Thread may be of help.
You will find stories about having problems because they said they are petsitting and, recently, there were two people who said they were allowed with no problems. Most people would probably advise booking accommodation and not mentioning petsitting, which is considered work and would not be allowed if you are entering as a tourist.
I have never been asked anything myself and have been three times recently within less than a year.
I hope this helps.