According to this account in La Stampa via an italian blog site, it's located " alledificio dellAnnona vaticana e accanto alla fontana della Galea - si estendeva lungo le pendici della collina al lato della Via Triumphalis."
I think Galea is a typo there & it's really the Fontana de Galera, or Fountain of the Sailing Ship (#17 on your map). The reference to the 'edificio dell'Annona' kinda throws me off though. It's not on vatican maps (Annonas are like ancient roman granaries, usually associated with municipal financial administration). I know that the Vatican Printing office bldg (#30 on your map) is sometimes referred to as "Spazzo Annonari". But the ancient Via Triumphalis (a short section of which is still called the Via Trionfale in modern Rome) that La Stampa refers to would probably extend over closer to the fountain.
My mom, who has spent a lot more time than I inside the walls of the Vatican & who has molto bene contacts there, thinks she heard it was way over by the vaticano railway station though. Sorry, I don't think she's right. I vote for this area right below (just SE of) the fountain where all the dusty white stuff is just inside the walls shown here on google maps.
Fontana della Galera
Thanks. I figured there would be someone on FR familiar enough with what's inside the Vatican City walls, to make an educated guess.