Within the first 10 seconds of both songs you can clearly hear very similar musical phrases played on a bright synth with delay and filter modulation. I didn't find any direct relation between the two songs and their production, but the similarity in that sample is so jarring, that I feel like there must be some kind of a relation.
Below is the information that I've been able to look up on the two songs.
もう歌しか聞こえない: Deaf to all but the Song is a remix/cover of もう歌しか聞こえない from the soundtrack of Imperishable Night -- an entry in the Touhou Project series of bullet-hell shooter games. The game was released in 2004. I don't hear the sample in the original. The remix/cover was first released in 2008 as part of album called Arrow Rain by Dark PHOENiX circle. Dark PHOENiX is a collaboration between 稲井ゆう(Yuu Inai), an arranger member of dojin music circle PHOENIX Project and 姫川紫音(Shion Himekawa) who seems to be a dojin arranger as well.
Courage is a part of the soundtrack for Dragon Ball Z: Ultimate Tenkaichi, also known as Dragon Ball: Ultimate Blast(ドラゴンボール アルティメットブラスト), a fighting video game based on the Dragon Ball manga/anime series, released in 2011. The game's music is credited to Hiroshi Takaki(高木 洋) who seems to have mostly worked on scores for various anime.
What I want to know is where that sample came from in both of the songs. Was there some influence between the two? Or are they both referencing some other song?
In addition to the links seen above, I've discovered the creators' personal sites. They're mostly in Japanese and my reading comprehension is not that good, but it might be possible to dig up on one of the blog posts quotes about from where they've drawn inspiration.
- 稲井ゆう(Yuu Inai)/Phoenix Project: http://p-pr.info/
- 姫川紫音(Shion Himekawa): http://peaceful-wind.sakura.ne.jp/SHA-FILE/blog.cgi?writer=sion
- Hiroshi Takaki(高木 洋): http://hiroshitakaki.com/