I bet iIt's not a stain it's etched from the cocktail and vinigar the only way to get it out is with diamond polishing. Not something you want to try without training. I've done several of these. Go to dirty grout and find a stone guy on your area and get him to do it with you as his helper ( good training) it's not going to be cheap though.
The JAGUAR 8.4 INDUSTRIAL SYSTEM; not your generic squirt & suck machine!