How do you know that?
How do you know it's an HC-05?
It doesn't look like one, but that doesn't necessarily mean that it isn't, and it doesn't look like an HC-06 either.
Why would they put an HC-05 in a car, and not an HC-06?
Could it actually be an HC-06? If it was, that might explain your problem, also the absence of the switch, and possibly your note that EN is not used. If you are cynical enough, you might even conclude it's neither, but actually a BLE device - which also would not use a switch or the EN pin. Identifying the chip might be helpful.
HC-06 is in AT mode by default @ 9600 baud, as are BLE devices.
I'm betting it's a BLE device......
This nonsensical post might actually be useful.