How are you related to this cousin? Who else is available to be tested and how are you related to them?

You have to track a male to male relationship from you back to your great grandfather, with no intervening females.

If you look at some of the messages here on this forum, you will see a heading about "creative thinking on relatives to test" which may give you some ideas.

My parents and all of their siblings are deceased. Here's what I have done to get the basic lineages of my four grandparents:

Maternal grandmother - my own mtDNA test
Maternal grandfather - my mother's brother's son's son was tested

Paternal grandmother - my father's sister's daughter's daughter was tested
Paternal grandfather - my father's brother's son was tested

Now I am thinking of how I can test back another line. My maternal grandfather's mother had a sister. Who had daughters, who had daughters who are still living. Testing one of those daughters would give me his mother's line.

My paternal grandfather's mother also had a sister, who had a daughter, who has daughters. Testing one of them would give me her line.

All I need to do now is get one of them to agree to the test.

The bottom line is you have to know someone who can be tested.