I put a Mitchell 308x reel on my 12' BGJP .... and to be honest with you, it's still a little tip heavy even with the 8.6oz reel. This rod is not the rear seat model, by the way (just in case yours is).
Now, I'm not going to be using my outfit to "vertical jig" with ... it's going to be for "flipping" double jig rigs for Livescope fishing.
I do have a Shakespeare Alpha UL reel on my 10' Sam Heaton rod, which is what I was using for that purpose (prior to getting the 12' BGJP) when fishing this way in a buddy's boat ... and it worked very well and is fairly balanced. But, two more feet of rod length does call for a heavier reel than that little UL, IMHO.