Proposition 13 does not target the elderly. It gives tax breaks to all property investors, including corporations and (due to Proposition 58) inherited estates.
[1] No doubt fanned by the usual anti-government, anti-civic rabble rousers that would eventually come to completely dominate politics.
Another way to determine who it targets is to suggest repealing it and watch who complains the loudest.
1) Elderly who bought early pay low tax, elderly who bought recently pay high tax
2) Younger people who are also rich pay high tax, but can afford it, and it is proportional to the amount of services they are receiving
3) Younger people who cant afford these property taxes are priced out of the area.