It is in bluez5-tools. Install with
devel-su
pkcon install bluez5-tools
Then start it (with root priviledges, i.e. after devel-su) with bluetoothctl
Then use the following commands:
scan on - to start scanning
When the car kit is discovered (its MAC address and name will be shown) type
pair [MAC address] to start pairing
then
trust [MAC address] to make the car kit a trusted device
and finally, if it disconnects and does not reconnect automatically
connect [MAC address] to reconnect, at which point it should discover and list UUIDs of your car kit’s Bluetooth profiles.
Then just leave it for a few minutes to synchronize data. Check after a few minutes in the car kit if there is phone book synced, if not, turn off the car kit (e.g. by removing the key in your car) or Bluetooth on the phone, then turn it on again and let them reconnect and do the sync by themselves.
As I wrote, in my case it required proper order and timing, so you may need to give it a few tries. Monitor blutoothctl’s output for whether the devices connect and stay connected during the process. If they disconnect, quickly reconnect them using connect [MAC address] before the car kit assumes timeout and cancels the pairing…