Yes - but in quite different circumstances. My stalker was coming to my house, making threats, intimidating me if I tried to go out (we lived in a small culdesac and I couldn’t leave without passing his house).
I had a dog, he got one too and like you he would always appear as soon as I left for a walk. Whilst this was part of the pattern of behaviour, it wouldn’t have been enough in its own right - everyone with a dog needs to walk it, often following the same route and a lot of people have similar daily routines. Even if it’s random times he could have chosen the same random time… I don’t mean to say it’s not deliberate in your case, but to meet the standard of a criminal court, this would be very hard to prove.
Is there any other behaviour of concern? Threats, approaches etc? Is he perhaps lonely and hoping for conversation? If you can understand his motive then it might help find the evidence to prove. Depending on his behaviour, it may not be appropriate to approach or ask him.
I don’t know the law on cameras/recording but I think there are rules about recording outside of your own property. Particularly if you are directing them at him or trying to record him, you could find that he has grounds to complain that you are harassing him.
The proof in my case came from audio recordings which I’d taken when he came to my house. I’d hit record on my phone genuinely scared of what he would do to me. I was told that that these wouldn’t usually be accepted by a court as they were taken without his knowledge, however it was very clear that I wasn’t leading/directing him - he did all the talking. And it was 6 years later before I had the courage to go to the police, so clearly no intent of a setup at the time.
I was fortunate to have an officer in charge who took things seriously from the start, but there’s a high bar to meet for proof in a criminal court and the CPS (or Fiscal in my case, I was in Scotland) won’t take a case forward if the evidence doesn’t meet the threshold. The police may be able to speak to him (and I think there are some measures they can take without arresting) to try and address things before they progress. I don’t think a lot of cases are taken as far as court, and conviction rates are not particularly high.
A note of caution - he is your neighbour and will (almost certainly) remain so. Whilst my neighbour was required to live at another address pending trial, this was unusual - normally he would have just been restricted from contacting/approaching. The trial lasted 3 days and I spent a total of 6 hours in the witness stand. It was harrowing. The stalking and harassment had lasted 6 years prior to that, and I had a complete breakdown in spite of proving him guilty. He had a non-harassment order placed on him. He continually breeched it, but Scottish law requires 2 sources of evidence for an allegation. We went back to court once, but ultimately I’d resorted to having a camera on every time I left the house, he still tormented me through the walls, I ultimately realised it would never end and moved house.
I really hope that you resolve things, stalking is an awful experience and I’m still wearing the scars several years on. Especially when it’s close to home and there’s no escape. Just take care, I know well that stalking behaviours can escalate, but don’t put yourself in a position for him to have a counter claim or it will make it very difficult to take further.