This ceremony is an American phenomena, it was invented by caterers and is the only of many creative ceremonies to have "stuck" from the early days of American Bar Mitzvah celebrations in ceremonial halls. You will find it across the spectrum of Jewish groups (including some Orthodox) but will generally only find it in ceremonial halls and not in synagogues or temples.
As I suspected this custom seems to have its origins in the birthday cake.
Many caterers, presenting themselves as religious specialists, expanded their repertoire to include ritual matters, not just culinary ones...
"There is a march, the bringing in of the Bar Mitzvah cake the lighting of thirteen candles, or of fourteen-one for luck..."
Invented from whole cloth (or cake), this affecting ritual transformed a widely performed activity-cutting a birthday cake-into a quasi-sacred event.
Joselit, Jenna Weissman. "Red-Letter Days." The Wonders of America: Reinventing Jewish Culture, 1880-1950. New York: H. Holt, 2002. 100. Print.