When the brochah shehakol is made on gum, is the brochah being made on the gum base, or the flavoring? (I'm assuming one makes a brochah on gum, but maybe not: see http://torahmusings.com/2010/11/chewing-gum-bracha-or-no-bracha/.)
It is on the flavouring. According to the famous Birkas Hashem (maamarim 1, quoted by the responsum on the topic - see below), there wouldn't be a need for a Bracha on flavourless gum.
People don't typicaly chew such gum today, choosing only flavoured gums.
While there are poskim (Birkas Hashem, maamarim 1) that hold that one does not recite a bracha before chewing gum, most follow R’ Ovadia Yosef (Yabia Omer 7 OC:33) and R’ Ephraim Greenblatt (Rivevos Ephraim 6:80:2) and recite shehakol.
Rav Yishak Yosef writes that you make the Beracha on the flavoring combining with the saliva.
The flavoring This is based on the psak of the rambam that one who sucks on sugar cane for flavor even though they are not eating anything still makes a shehakol.