A fall is usually the case with hillwalkers. It's looking less likely here now. Why? Cops don't think it is and the partner's story has absurdly large gaps and inconsistencies in it. Although partner denies it, she had certainly left him, perhaps temporarily, and told a fellow walker as much. Suicide is possible. But the most likely thing, imho, is that her partner had access to a vehicle and drove down to see her excited at media coverage on the day she disappeared and hoping this may change her mind about staying away. Left his phone at the gite but had another. Rang her asking to meet at the campervan when he got to her area, most likely on 23 Nov. She acceded and met him there. She would not go home to him and they argued; he lost his head and strangled her. Drove home, burying the body somewhere shallow and near a road on the way home.
Cops will finish latest hill search then start to look for the car. They'll need to check thousands of local residences accessible by bike, and check with second homers residing all over Europe asking if the partner had an open agreement to use an old car at their location. Or if they have a car the partner may have known about which could be used in their absence without their noticing (plenty of second homers have an old banger, often with keys in, they wouldn't know had been moved). I don't doubt cops already have quite a bit to go on - possibly a radio silence on his main phone. They'll be tracing all cars caught on cameras en route; checking all cellphone numbers which pinged on location masts. It's massively manpower intensive and expensive, though. They'd likely prefer to let him hang himself, exploit his obvious psychological wobbliness, offer manslaughter and get him to fess up. French/Spanish cops usually happy play the very long game. UK cops less so - they've made no comment whatever, interestingly. Cops have kept the campervan as possible crime scene evidence. They'll have kept partner's devices too.
Re; my last. Missing detail. Fine line between being psycho enough to strangle your partner in a rage, and considering it in advance. I think, from details in public domain, that he thought he might kill her if she didn't agree to come home and so left his phone at gate. Would amount to top murder but prosecutors wouldn't get that through on basis of the phone alone. He has a history of mental illness and on that basis I think he'll be offered manslaughter if he fesses.