A question for biblical history-buffs: Where did the holy sponge come from?

For the sake of my argument, let's treat the Bible as historically correct.

https://en.wikipedia.org/wiki/Holy_Sponge

The scene:

A few roman soldiers, on tour of duty in the occupied province Palestine, formerly the kingdom Israel, get assigned to stand guard at the execution-hill outside Jerusalem. Golgotha. Where people get executed the way that is customary for rebels in the Roman Empire: crucifixion. For years now there has been on and off insurgent activity by a group of jewish rebels called "zelots" and accordingly the roman soldiers are in full armor. It's a hot day, so the soldiers got provided with a ration of a traditional roman refreshing beverage: Water with a dash of wine-vinegar in it.
https://en.wikipedia.org/wiki/Posca
(Lemons were already widely known in Rome, but as a medical substance, not for refreshment. There was no lemonade in Ancient Rome.)

One of the dying rebels is a man named Yeshua, a wandering priest and religious fanatic who has disturbed the peace by giving the pharisees trouble. Eventually, the soldiers decide to give him some of their vinegar-water to drink, by tying a sponge to a stick or branch and holding it up to his mouth.



My question is: Where did this sponge come from?

The Bible simply says that one of the soldiers ran and fetched it, but from where? Where do you find a processed and ready-to-use sea-sponge at the edge of the city? And at the execution-hill at that?





The most obvious explanation is bad storytelling by people who wrote this scene long after it supposedly did or didn't happen. But let's keep on treating the Bible as a historical document.

Where would you find a sponge in a roman city?

https://en.wikipedia.org/wiki/Xylospongium
In a toilet. The Romans used a sponge-on-a-stick to wipe their ass after taking a shit and disinfected it afterwards by putting it in a jar with vinegar next to the toilet-bowl, ready for use for the next guy.





A sponge.
On a stick.
Soaked in vinegar.
And roman soldiers looking for some fun shove it into the face of a dying insurrectionist who thinks he's the Son of God.