The reason the hand sanitizer works is because it's got alcohol in it. You can try just rubbing alcohol on it. Just be careful to test anything you use on the carpet somewhere hidden since your carpet is brown. Some things may lighten the color of your carpet.
Another suggestion is to mix some Dawn dish soap with water. Pour some of this on the stain. Get a white rag (or paper towels), get it damp with water, and lay this over the stain. Heat an iron to cotton setting & then iron the rag or paper towel in order to steam the stain. Be sure to keep the rag/towel wet!!!
I've used that trick on orange gatorade (long after it was spilled...) and black Sharpie on carpet.