In my experience, I've always been able to get the Caliburn a few days after completing Ghost Town and it's associated follow-up quests (Lightning Breaks and Life During Wartime, I think). I personally don't ever use the "wait" option, and instead, I just do other quests. Once Life During Wartime is complete, I head back into the city to do other quests, and by the time I get a call from Panam for her next quest, the Caliburn is usually there.
To be on the safe side, travel back into Night City and don't return to the Badlands for a few days and the car should spawn.
I know the other free car in the badlands (the colby butte) seems to be glitched where if you don't obtain in when you first enter the badlands, it seems to despawn after a certain amount of time. Perhaps the same thing happens to the Caliburn if it spawns and you don't return to it until the end of the game.