It's a tricky one OP. You don't mention what HE is inclined to do? Don't worry about the neighbour. Nobody can tell him really. Has he actually mentioned to you about re-applying?
I'm probably slightly biased as I have a DS who applied to C with four A* - he was pooled but rejected. Got places at Durham, UCL, Exeter and Bath. But after results day when he achieved his predicted grades, he decided to take a gap year and was accepted to C in the following Jan. He had done a lot in terms of "super curriculars" by this point though. His PS was much better second time round. But not only that, the gap year experiences were the best thing he's ever did (in his words). They talked quite a lot about his voluntary work in the interview because by that time, he'd already been overseas for three months. He had about 5 friends from his school (quite well-known selective independent day school) who all reapplied to Oxbridge for various courses and all were successful second time around.
So IF your DS takes a gap year, I'd recommend having a clear plan and structure for it, so that it's worth doing in its own right, regardless of Oxbridge.
To be honest, I realise now (and so does DS) that he was in a very competitive school environment which, on occasions, bordered on toxic. Once he was out of all that, he realised what a nonsense the whole uni league tables thing is - first world problems for sure! He really grew up a lot in the six months since leaving school snd I know, even if Cambridge hadn't worked out again, he would have been 100% happy to go to UCL or elsewhere. It's amazing how, when they get out of their environment, the mindset changes!
Having said this, he's had an incredible year he would never otherwise have known. He's more mature and resilient now and I think he'll cope much better with uni. Well I hope so!
Its August now and the ENGAA and interviews will come around again in no time at all. It's possible he could have an unconditional from Cambridge (and other unis) by Jan. That's only 5 months and it flies by. Its so much easier applying second time around as they have a much better idea about the whole process, the different colleges, etc. No need to choose an insurance either. Unconditional offers are great because then they have months to enjoy the rest of the year and can really look forward to uni without exam stress.
Just in case you didn't know, for many courses at C, if you apply with at least three A* achieved, it's automatic pooling (which obviously means they are guaranteed an interview). I'm not sure if engineering is included though?
But ultimately it's up to him, My DS felt as if C was his dream so it was worth the second shot, otherwise he'd always have wondered "What if?" But your DS may not be that bothered. I think, all you can do is let him know you will support him either way and he will know what's right for him.
Congratulations to him on his results too!