Invert ground vs. open "signal" - relay?
You're saying the ABS logic has been reversed in that one system pulls low to indicate 'ABS on' and the other pulls low to indicate 'ABS off'. Your schematic is correct.

Good practice when switching a relay from an electronic device is to add a flyback diode to catch the negative inductive kick that the relay gives on turn-off.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The complete circuit with lamp and guess of likely ABS unit internal transistor switch.