compatible signs according to month of birth according to Bazi

I would like to ask you a question.
I was born a year of the Rat but my day master sign is Monkey.
Some astrologers say that the main personality is given by the sign of the Day Master.
If it is true, it would be also logical that we search a compatible sign in accordance to our day master sign.
I consider your boards “Find your compatible zodiac signs according to your month:“
And so I wonder if as a male born on May a year of rat, on a day master of Monkey, I have to search on the board corresponding to Boy's match for rat or to the board corresponding to Boy's match for Monkey.
And if it is the board of Monkey which I have to consider, I wonder also if I have to taking account also of the Day Master of the sign which suit to a Monkey born on May.

To resume my question, do I have to consider.
1- Rat born on May > Boy's match = Cow. So the companion would be a woman born in a year of Cow
Or
2- my Day Master= Monkey born on May > Boy's match = Horse. So in this case, I wonder if the companion wouldn't be a woman with a Day Master of the sign of Horse.

Thank you by advance for your explanation.

Jean(John) Paul