I did hospital visiting in Selly Oak in Brum for returning injured service personnel. I found that a lot of the lads wanted to not talk about what had happened (except in the last five minutes of a visit) we had a good laugh talking a lot about bushcraft and knotting and hammocks and bad kit. A lot about bad kit and good kit, I mean a lot, they give people in this forum a real run for their money.
with one bloke I talked about game keeping and poaching - he'd done both a fair amount. We talked a lot about good places to visit in the UK - this was sometimes a way for people to talk about the injury they'd sustained - would they be able to get up a hill, what about not being able to see properly anymore, were there good pubs.
Sometimes the bloke I'd be with would just be furious about something and would only grind stuff out. But that was ok. It was ok for him to be furious, it was a pretty furious making experience he'd had.
I only talked with people who wanted someone to talk with them even if when it came to it they wanted me to talk and them to listen - I had a mental list in advance of stuff that might be interesting - books, something on the radio, camping disasters, bushcraft, food foraging, films I'd seen. With one guy he wanted me to read all the Just William books - his mum read him them when he was a kid, he'd been blinded by an ied and having a nice middle aged lady read to him worked for him.
I've worked with a lot of ex-servicemen in prison and in adult education - almost all had a sense of humour - dark, mucky, crazy, sardonic - but there, almost all had some great stories, almost everyone I met had had ptsd to a greater or lesser degree (by their admission not by me guessing), almost all hated how crap and empty it felt being out and struggled to find mates - and that the legion was all people my dads age (nearly ninety) so ok if you were looking for a grandad figure! Quite a few felt like something had gone badly wrong between going into service and coming out in the rest of the world.
One of the lads I visited in hospital started writing to someone on death row in the US - he found a way to be useful in his own eyes, and got to chat with someone worse off with him - his words. He felt it stopped him being a ****.
So, your neighbour. Sounds like you're doing the reaching out - he may or may not respond - not all who wander are lost, he may be ok, but he might not be and what you're doing might be the thing he needs right now.. Good on you.