This sort of thing happened to a colleague and she was reluctant to go to the police.
Her ex would send messages in whatever way he thought they would get through. She blocked him, she changed her number, she used a different name on social media, he still kept getting through to her.
When she stopped him from contacting her one way, he found another. Eventually he had to resort to asking other people to pass on messages and information.
He was like your ex in that he would go quiet for a few days and then send a barrage of messages.
The police did take it seriously, and after she had spoken to them and they checked his name and address they realised he'd done the same thing before and was known to them.
She took printouts and screen shots of his messages, even the ones that just seemed like he was saying hello or asking how she was. It's still unwanted contact and the intention was to let her know he could still get to her, so it wasn't dismissed as just a greeting, they still considered it harassment.
The police warned him off, and it worked.
It might sound like it's not serious, but it's bothering you and he knows you don't want it.
In my own experience, we've gone NC with family members, and they refuse to accept this.
They send gifts we don't want, and then pretend they don't understand why we aren't pleased with them, because what's wrong with sending a present? Presents are nice, how could that upset anybody?
Or they put appeals on Facebook. If anybody could ask Hygge or Mr Hygge to call us, we haven't heard from them in a while and we'd like to hear their voices. We miss them.
It makes it sound like we've just been a bit slack in keeping in touch, and not that they know we don't want to speak to them at all, ever. Then some well meaning friend or relative lets us know so we can call them and we have to explain to a growing circle of people that we really don't want to know.
They think that because it's presents and nice messages, there's nothing wrong with it. It's actually really stressful and upsetting, and just recently they used the a particularly upsetting date, the anniversary of our child's death, to drop off a Christmas card and present, then got upset when it was returned to them.
I have now warned them that if they get in touch again we will start legal action to keep them away. From what I've learned, what they say doesn't matter so much as the effect it's having on us, and because we've repeatedly asked them to stop all contact, that matters more than what the contact is.
They think they have some kind of loophole because they're sending nice presents not nasty messages, but apparently that's not how it works.
I think you might need to look into doing the same thing. We have been told that if we don't want to immediately try for a restraining order we can do a cease and desist letter. You can send one yourself or have one sent via a solicitor, and we think that's what we will do. They haven't listened to us, so I think a solicitors letter will carry more weight. You only need to prove two instances of what a reasonable person would consider harassment, and it's also a way to formally record the request to leave you in peace.
Don't respond to anything else he sends to you though. Ignore but keep it, and either contact the police or consider a solicitors letter. I hope you'll be okay.