Hello and welcome to Just Answer. My name is ***** ***** I will be happy to assist you with your electrical question.
1) If you purchased a pull chain replacement switch at Home Depot or Lowe's, these seldom work. Even though a pull chain switch may look similar on the outside, the inside of the switch can have a different switching pattern and the universal switch that was purchased may not work correctly.
2) Unfortunately on ceiling fans, there is no standard color code for pull chain switches. Hopefully, you labeled the wires or took a picture of the terminations prior to disconnecting them from the original pull chain switch?
Often, but not always, Black is used for the hot wire, Grey = Position #1, Brown = Position #2 and Purple = Position # *****
See attachment shown below:
3) If the switch you purchased does not work, I recommend that you contact Gulf Fans as shown in the link below. Provide them with the manufacturer name and fan model number and they can send you the correct pull chain replacement for your fan model.