The funniest puns occur accidentally.
As someone known for bad jokes, I can tell you that when I pun by accident it is much better received.
We had a good laugh at the office years ago when the tennis player Billy Jean King was first accused of being a lesbian. I was asked if I believed it and I said that it was likely true....why would anyone accuse her of that if she wasn’t? It would be rather fruitless. I didn’t even clue in until they started laughing.
As someone known for bad jokes, I can tell you that when I pun by accident it is much better received.
Accidentally? You really need to deliberately have more pun in your life.