A quick note:
A few things are arbitrary. You can have both side of the motor connected to ground or both connected to +12 when teh relays are off.
You can have a closure to ground move the relay or a closure to +12 turn on a relay.
Both relays ON or both relays OFF mean motor stopped and operating into a short (dynamic braking).
A small diode e.g. 1n4001, 1n4002 should go across the relay coil in a way that it doesn't conduct.
The contact numbering has meanings and there are two different pin-outs of the automotive relays. If you follow the numbering scheme, them a relay with an internal diode won;t blow up if used as a replacement.
The installed diodes should go close to the coils. The diodes "protect" any solid state devices driving them.