Depends on if you were playing RPGs or not, although action games were full of it also. Look at Contra 3s final boss, there are like 3. You also have the terminator boss in contra 3 that has a fake boss before the real one.
I didn't play that many RPGs, but I did notice when they did this.
Parasite Eve 1 has a fake out final boss.
Contra Hard Corps did a few more fake/extra phases and fake out bosses depending on what choices you make and what stages you chose. Those can at least be excused for being new/newish at the time. They at least do them in clever ways, or don't have health meters. Like the Agni and Rudra fight from Devil May Cry 3, if you kill one, but leave the other enough alive.
The only modern non-Souls games that do health bar fake outs are
Streets of Rage 4 with the dual boss fight against the Y Twins and Osiric from
Final Vendetta.