My experience in learning Japanese pitch accent was eye-opening. At the start, I couldn't hear any difference. On quizzes I essentially scored the same as random guessing.
The first thing that helped me a lot was noticing how there were things in my native language (English) that used pitch information. For example, "uh-oh" has a high-low pitch. If you say it wrong it sounds very strange. "Uh-huh" to show understanding goes low-high. Again, if you reverse it it sounds unusual.
The next part was just doing lots of practice with minimal pairs. Each time I would listen and try my best to work out where the pitch changed. This took quite a lot of time. I feel like massed practice (many hours in a day) helped me more than trying to do 10 minutes regularly. Try to hear them correctly, but don't try too hard. I didn't have any luck with trying harder to 'understand' what was going on. I liken it to trying to learn to see a new color. There isn't much conscious thought.
The final piece of the puzzle was learning phrases, not individual words, that had pitch changes. For example: "yudetamago" could be boiled egg or boiled grandchildren. Somehow my brain just had a much easier time latching on to multi-word phrases instead of single words. Listening to kaki (persimmon) vs kaki (oyster) again and again seemed much harder.
Of course, your mileage may vary with these techniques. I already spoke decent Japanese when I started doing this.