There's also Kris Kross' song named "Jump" too.
Which fits to the Gao shark cutter being a pair.

And House of Pain's "Jump Around" too. Which has lyrics that rather match what the Gao Cutters are described as.
Is there any set era to how songs are decided or discernible pattern to them? Genre?

A vast majority of them are classic rock and pop music from the 80s and prior with a few exceptions maybe. Heck even I was amazed after a few months at how many of these are likely to appear on some oldies station while driving. :lolol
In the case of multiple entries I try to narrow it down based on the current pool of references on how well-known it is and how well did it chart at the time it was out.

Okay, well both of the other "Jumps" were early 90s and chart toppers. 92 for one of them, maybe near both. They were played out the wazoo in America at least to the point even elementary school kids heard them pretty constantly. Not sure about Japan. But they were both one of those "overplayed to death" style songs in America. More hip hop than rock. But that also kind of fits with the whole "Jump" theme.

The audio drama on the first soundtrack. It might not have a song connection because it's for supplemental material, but it's probably based on the Gosei microphone from Akibaranger (unofficial sentai inspires an unofficial piece). It has a weird power too - forces people to speak only in rhyming rap.

Normally I try to maintain a one track policy but I guess in this case I will have to make an exception until there is some definitive tracklist by the creators of the show, cause you do have a point and this particular one is, like I said, a bit of a doozy and unclear compared to most of the ones archived so far. And to be honest, I was probably of one out of the millions of kids who jumped like a lunatic to that song during birthday parties. :lolol
Updated.

Hmm, I will keep it in mind but for now I will postpone archiving it unless they give us the definitive Japanese name and the French name at least, and also show us what it looks like.

New update this week. This time, that tune sung by a cat... wait, what?
http://www.tokunation.com/showpost.p...24&postcount=1

Wait, this means there are two Go-Busters items?

Yep. Sougan blade was a while back.

New update this week. This time, flowers.
http://www.tokunation.com/showpost.p...24&postcount=1

So side note, I think this one is probably the first time the collection name is identical to the song it is referring to. :)

I'm feeling pretty convinced that either of the two Go-Busters items isn't actually from Go-Busters... but I haven't found anything in any of the series that haven't been used.