Donna,
I have 2 suggestions. Have this cousin contact your gf and tell him you have been trying to contact him and the 'enforcers' haven't even let him know. I would also send a little note/card to let him know you're thinking of him, if you want want to do it.
I would also wonder why your mother left and never bothered to contact them again. It seems very extreme and perhaps she had a very good reason for endings things. If you haven't had a great feeling yourself to contact him, maybe you should go w/ that.
As a young child, I stayed w/ my maternal grands, till they and my parents had a falling out. Didn't see them again till I was about 15 yrs old. My gf stepped over a line, it ruined any sentimental views I had of him. My mother could never see this about her father. I didn't bother to see him again, until he passed away - 2 wks before I got married. My mother was very upset that I wouldn't go see him in the hosp. She has never gotten how upset I was by his behavior. I went to his funeral FOR my mother, nothing more.
Donna, I am not prying, pls don't think that is my intent. I just meant there may be a reason, he hasn't even contacted you all these yrs. Bottom line, don't let anyone push you to 'connect', do what is comfortable for you. You don't need to answer to anyone, cousin or not.
I wish you the best.
God bless. Alice.