I've never seen the Dragoon at the Volcano, but at Bed Desert there was a Red Dragon VS Green Dragons and maybe an Archer or an Oracle. The Red Dragon usually goes after the Archer/Oracle first, except for when my Math Skill/Setiemson/Two-Wizard-Rod Summoner Holy'd the Oracle!

Also, I've has a Dragoon girl on my side at Mandalia against a male Archer, another Dragoon girl, some Gobbledegucks and a Vampire. But that Dragoon wasn't pumped...

Once at Mandalia, I had a different Chocobo-guest battle coming from Igros. It was named Snow Wind and it was able to join for some reason...

And who can forget the Green Dragons guests VS Blue Dragons led by a lone Red, again at Mandalia?

Now, if only there was a guest Calculator battle...

Also... regarding Invite... in the Save Cloud battle, I noticed it to be somewhat easier to Invite. Strange... Invite seems to succeed more in this battle. I might've just been lucky, however...