My first thoughts were alcohol and hairspray. One of my sons had a fountain pen in his pocket, left it in his pants, and it leaked thru the pants onto his bedroom carpet. I tried alcohol which just made it run. The man who cleans my carpets was able to get it out. I have no idea what he used but maybe someone in your area might be able to help. Sometimes, our cleaners have been able to remove stains I could not at home--maybe see what they think.
HTH,