Could it be that Jimmy Gordon ''Buzzzzzz'' connected to Peter Pan & the Good Fairies? He is credited with writing both sides and I read online that it's a possible.
Yes, it's good; and so are a lot of grunge, jazz, hip-hop, death metal, etc songs. However, that doesn't qualify them as garage, so I agree with Mikael.
It has a Doors vibe to it, so I'd say it's a pop instro (I've never considered Doors garage). Buzzzzzz is a straight R & B instro, and "yes" to your final last question, at least it sounds like it to me.