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.

New update this week. This time, ancient stuff and hi-tech stuff.
http://www.tokunation.com/showpost.p...24&postcount=1

Also, a correction regarding the collection La Vie en Rose. Turns out it was not the Dyna Brace but the Rose Saber.

Plus we also got a collection piece based off the Mobirate from Gokaiger.

I will keep it in mind. ;)
However I will update it when TV Asahi gives us the details on their website since that is what I am basing it off of.

Yep. Goody called it Bad Boys, so I'm assuming it's based on the song by Inner Circle (the theme from Cops)

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

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

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

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

New update this week. This time, 3-3-5.
http://www.tokunation.com/showpost.p...24&postcount=1

Since "(The) Wise man/L'homme sage" Lupin Collection are based off the Megaranger's Degitaizer, Pekka increasing his intellegence might reference to how Miku Imamura (MegaPink) was upgraded to Super Miku when she become more intelligent and powerful in Megaranger Episode 17.

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

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

New update this week. This time, we fly.
http://www.tokunation.com/showpost.p...24&postcount=1
So episode 39's collection of the week is a real unique one in that it is not a prop from the show it is referring to, in this case Jetman. They actually referred to a scene from the opening of the show which is pretty interesting. I was at first thinking "Maybe this is a reference to the cross changer's pentagon-shaped bracelet" but that seemed too abstract. The concensus so far in Japan seems to be the scene from the opening theme and I agree.

We almost reaching to 40 episodes and I think Gorenger, JAKQ, and Battle Fever J Lupin Collection is owned by Dogranio, Zamigo, and Destra.

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

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

The piece that was apparently stolen (going by the illustration seen) is based on AbareKiller's Wing Pentact from Abaranger, It's name is
Le Maître Des Marionnettes, an homage to the Metallica song Master of Puppets.

Good find, I will make sure to credit you when I update the first post after we get the official TV Asahi description of the collection. :rock:

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

Shout outs to jimb85 for you know what. Good find.

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

According to the Ranger Wiki, some of the collection pieces from the movies are:

Welcome to the jungle/Bienvenue dans la jungle - based on the Ginga Brace from Gingaman, it creates vines that can bind opponents. Name comes from Guns 'n' Roses' "Welcome to the Jungle"

Meteorite Fall/Météorite osei - based on the Saiko Kyutama from Kyuranger, it summons meteors to rain down on opponents. Name comes from "Shooting Star", though this is a song title that's been used by Bob Dylan, Elton John, Lou Reed, and Bad Company

New update this week. This time, nothing from TV since they are taking a break. But I updated the list with the two movie collections. Shoutouts to jimb85.
http://www.tokunation.com/showpost.p...24&postcount=1

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

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

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

New update this week. Adieu.

http://www.tokunation.com/showpost.p...24&postcount=1

So...they didn't make Gorenger Lupin Collection and JAKQ Lupin Collection in the series. Maybe for V-Cinema or VS Movie?

Just some final additions - based on the descriptions in the collection catalog, Red Dial Fighter's official name is La zone de danger (after Kenny Loggins' song Danger Zone) and the VS Changer is called Changer le monde (after the Eric Clapton song Change the World)

Didn't expect to be posting on this thread again, but news has dropped about the collection pieces from the LuPat/Kyuranger movie, so I figured I'd help add them

Le feu inoubliable (The Unforgettable Fire) - named after the U2 song of the same name. Lets the user create a flaming whirlwind

Le bois norvègien (Norwegian Wood) - named after the Beatles song of the same name. Lets the user summon logs to use as projectiles

Une autre brique dans le mur (Another Brick in the Wall) - named after the Pink Floyd song of the same name. Lets the user summon bricks to use as projectiles

http://www.tokunation.com/showpost.p...24&postcount=1
Some extra finds updated.

I just want you to know jimb85 that I updated some of the descriptions for your finds based on the Japanese text I found for them, but either way please know that I give you credit for finding them. Thank you. :)