Xanthan gum should supposedly be good for this purpose, however I have not tried it since I had trouble finding a place to buy it. I found one online shop, but it was quite expensive so I experimented with corn starch instead which is very cheap and readily available. It worked, however it is a little trickier to deal with than xanthan gum, which can just be added directly.
If you decide to try corn starch, I would recommend to first make the thickener using water and starch. I cannot remember the ratio you need, but try it out. Both ingredients are cheap.

Put some water in a cup, add some starch, stir until dissoved and heat it up in the microwave (or use a pot on your stove). Take it out and stir regularly. When it reaches a certain temperature, the starch will react, the mixture will thicken and become transparent. Here you can adjust the thickness by adding water/starch and reheat. Be careful not to make it boil, or it can make a mess (hence why it is good to take it out, check and stir every so often). You will want it quite thick (so a spoon can stand by itself in it) so it can be added straight to the Vanish without diluting it too much. If you make it in a pot, I would be even more careful about letting it boil it since the squirts could probably give you some nice burns since it sticks like napalm..
This is how I made a gel from hydrogen peroxide when I last needed to treat some cases. I will probably try with pure Vanish next time since it is easier and probably safer to use.
Edit: An extra note regarding using corn starch - when I used it with peroxide it seemed to become thinner as time went by. It was good for most of the day, but the next day it was much thinner. Maybe the starch molecules was torn apart by the peroxide? Anyway, it worked for as long as I needed it.