How to extract mouth numbing effect from Sichuan peppercorn into a syrup?

After reading @bob1's very helpful answer I ran a couple tests and found that the hydroxy alpha sanshool does seem to be soluble in alcohol such that it could be infused. In my first test I left a pinch of peppercorn in a splash of 80 proof vodka (didn't measure either) and left it for around 6-8 hours. It tasted horrible but did numb my mouth. In my second test I left a tablespoon of red peppercorn in 80ml of 84 proof mezcal for about 18 hours, which again did numb my mouth although not as strongly. I also chewed on a couple of the leftover peppercorn which had no effect, leading me to believe I did successfully extract the hydroxy alpha sanshool.

My final conclusion to my question is that trying to get the mouth numbing effect into a water and sugar based syrup is not worthwhile or really even possible, but you definitely can get the effect into a cocktail by infusing alcohol.

The reason you didn't get the numbing effect is because the hydroxy alpha sanshool is an alcohol that is largely soluble in oils not water.

When boiled it will come off in the steam and escape the boiling process in that manner. If you distill it, it will collect as an oil not as an ethanol/water soluble product. I doubt that putting the lid on the pot will collect significant amounts, or if they do collect enough to form droplets, they will be as fine oil layer on the surface of the liquid or on the lid of the pot.

I note that the extraction protocol mentioned on its wikipedia page includes ethanol and notes that the yield is low (~60%) of the available chemical. Boiling alone in water is not sufficient to extract any significant quantity.