There are plenty of well-used tropes in the Japanese drama whether it be the sage hat-wearing detective who finally brings a criminal in for justice or that colleague at the company who lives to snark or bully the protagonist. Another trope: the fateful scene of two "will they or won't they" characters meeting at night in the middle of a cloudburst as a cliffhanger until the next week's episode. It would probably take a week to dry out all that clothing, in any event.
Up to now, there has only been that one article devoted to singer-songwriter Nobuo Ariga（有賀啓雄）which was written up by nikala for the atmospheric "Rain Dolphin". Well, I finally see her article and raise her "Ameiro no Boku to Kimi" which was Ariga's debut single from 1987.
The direct translation of the title would be "Rain-Coloured Me and You" but of course that sounds somewhat Google Translate-ish, so I will go with "You and Me in the Rain". The song starts off sounding rather folksy but then with a crisp rat-a-tat of the drums, it goes into a fairly brisk run as a mid-tempo pop tune about a man being called up by a woman to meet her all of a sudden while the rain is pouring down. According to Ariga's lyrics, the impression is that the woman is already in another relationship so the man could be a former flame or a good friend (who really wanted something more with the woman). In any case, he's pretty annoyed at the request but still heads on out. That rather does sound like a scene from a drama.
"Ameiro no Boku to Kimi" was also a track on Ariga's debut album "Sherbet" also from 1987. It's perhaps coincidental that nikala and I would pick two songs in his discography that sound pretty atmospheric with rain in the title. I rather wonder if this would be a theme with Ariga.