Substituting invert sugar for corn syrup
The website you gave has a page for corn syrup, suggesting substitutions. It suggests the following:

1/2 cup sugar + 2 tbsp water = 1/2 cup light corn syrup;

or

1/2 cup honey = 1/2 cup light corn syrup

This is a good start, but to be more precise you might want to dig in the composition of light corn syrup. The USDA National Nutrient Database suggests the following composition (by mass) for light corn syrup:

23% water
77% sugars

The composition of those sugars varies from a corn syrup to another. Wikipedia lists four common High Fructose Corn Syrups (HFCS) standards, namely :

HFCS 42, 55, 65 and 90

The number represents the mass percentage of fructose once the water is removed. HFCS 42 is said to be the one usually used in 'baked goods', so aiming for 42% fructose seems like what you may want to be 'chemically similar' as you said.

Honey is not a perfect substitute as it contains less water (17%) and different sugars, but water it down a bit (add 8g of water for 100g of honey) and it could do the trick. Of courses different honeys will probably have very different water content, so unless this water content is written on the product the best available solution is probably to just try to get the same thickness as corn syrup as best as you can, slowly adding water.

Apparently the average honey, once the water is removed, contains 50% fructose and 44% glucose (the remaining few percent's are other sugars such as galactose, maltose and sucrose). This is probably close enough to the 42% fructose 58% glucose of corn syrup.

Inverted sugar is precisely 50% glucose 50% fructose, so like honey it will give something similar to corn syrup, but not exactly. Adding 30g of water to 100g of inverted sugar will give you a syrup with 23% water content which should be a good substitute to corn syrup.

The suggestion made on the website to use 1/2 cup sugar + 2 tbsp water in place of 1/2 cup light corn syrup will give you something more chemically different than using honey or inverted sugar. Corn syrup is fructose and glucose, usual table sugar is sucrose, a molecule formed by gluing a glucose and a fructose molecule together. It might make no difference in this particular recipe, but it just is chemically different, so the other options might be better substitutes.

Finally, if as you said you want to start from just sugar and water, partially inverted sugar can be done at home by heating up a sucrose/water solution with a bit of acidity. Now, if you want to really have the right water content of 23%, my tactic would be to mix 100g of sucrose with 30g of water (of which some could be lemon juice, but then you might have to add a bit of baking soda to correct for the acidity if that might become a problem later in your recipe...) and put that in a sealed container that I would put in the oven for a couple of hours at 114°C (237°F) (a bit more should be ok, but be wary that the container will experience high internal pressures, and that all the more that you increase temperature. Manipulating and especially opening the jar while it is still hot might be dangerous).

Most recipes on the web call for having a higher initial water content and boiling the mixture at this temperature, I have no idea if this is somehow more efficient, but clearly you will end up not knowing the final water content, unless, and this might be a good idea, you weight your saucepan with only the sugar in (say 1kg) (call that mass M), add 480g of water and boil that for a while with 1g of cream of tartar as I saw on this website, and at the end of the procedure boil a little longer or add a bit more water until your syrup weights M+300g, at which point it should be a good substitute.