How to turn sugar syrup into sugaring wax?
I think if you start with regular sugar syrup, you have too much liquid. I make sugaring wax by putting 8 parts sugar, 1 part water and 1 part lemon juice in a sauce pan and let that simmer for about 10-15 minutes until you have an amber colour.

It will take a couple of times to judge the mixture on thickness and colour. Once it's set, you should be able to push a finger in it and that mark should stay there for a couple of minutes.

If your mixture is too pale, it's going to be too liquid and the finger mark will disappear too quickly. You can just put it back on the stove and let it boil for a bit longer.
If your mixture is too dark, it's going to be too hard. You will be able to make the finger mark, but it's gonna be hard to do. You can reheat the mixture in the microwave and use it warm.

Depending on how you want to use it, cooking times are more or less forgiving.