IS the heater core the black rectangle on the right hand side or the group of vents in the center?

 

it looks like you have AC. from right-to-left, is tha:

- blower box
- AC box
- heater box

your heater core is in tha heater box. (box in center of firewall.) it's located within that box, but at tha bottom. it's made of copper. it looks like a tiny motorcycle radiator.

_taF