[...] I have never read a patent before so I'm confused
Be reassured that people who have read patents before are confused too. More so if the patent was written by an attorney. It often helps to start reading at the claims, which constitute the last section of a patent, even before reading the introduction.
You need something that acts like a soap. A rather long molecules, with a non-polar tail (binds the paraffin) comprising generally C and H, and a polar head (binds the water) with additional atoms like O in functions like alcohol, ester, salt and similar. Traditional soaps are salts of a fatty acid obtained from a triglyceride (oil or grease).
The patent seems to use several such molecules of varied lengths. This could be a trick. Plain soap emulsifies grease in water, but paraffin is a more difficult target for being completely non-polar. Maybe several molecules bridge from paraffin to water in several steps, the longer molecules binding better with paraffin and the shorter ones with water. Just a hypothesis from me.
The patent not only mixes several molecules. It also saponifies some triglyceride(s) and brings additional glycerine or glycol before mixing with an additional fatty acid. Transesterification should happen, where glycerine reacts with acids of varied sizes. Some soap seems to remain. This complexity may be a key to bind the very different paraffin and water.
I wonder if such a formulation is good as an encaustic. Encaustic is to act as a water repellent
, to my understanding. The patent's heavy molecules used for the emulsion won't evaporate but stay in the encaustic and help to bind water, which isn't desired.
My first thought would be to avoid water. Use a hydrocarbon solvent, non-toxic and evaporating slowly (but it's a fire hazard), that leaves just the paraffin on wood. I understand this is not your present task.
Even in a water emulsion, I'd try hard to add only volatile molecules
, to leave just the paraffin after drying. Ideally, they would evaporate at the same pace as water. Rather short mono-alcohols would fit, if they achieve the emulsion, for which a mixture of several sizes may help. Esters would be more volatile, asymmetrical to help the emulsion.