OK, one more tiny shot at humor;
It really doesn't matter WHAT you call it,
it won't come to you when you call it.
Ha Harr...
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I have a Hillsborough aluminum flatbed on a 1 ton frame, it has the trap door with gooseneck ball installed.
All this works very well for me and has done so for over 6 years.
Having a full width bed over has been much more convenient than just a 4ft or so wide space between wheel wells.
So much easier to toss couches and stuff on from the side for casual furniture moves.
NO questions of clearance between the underside of the trailer and the top of the truck bed sides.
No tailgate to mess with - and forget it is still down until the first sharp turn after hooking up.
{If you see folk with gooseneck or mini 5th trailers and no tailgate - don't ask whu they took it off (-: }
When I tow I just flip the trap door open, back under the trailer, etc.
There has never been a "grease the dog" (which then greases the house) scenario.
From time to time I have been asked to move campers to/from seasonal sites for folk who don't know the difference between (mini)5'th wheel and gooseneck.
I like helping people out and once in a while it doesn't bother me if I spend a few bux and don't get it back.
I have no interest in obtaining insurance coverage for this and since these trips would typically cross State lines... to do it for anything more than exact out of pocket expenses would classify it as interstate commercial hauling. So insurance would be HIGH to haul a couple of other folks' trailers say 100 miles each way a couple of times a year.
OK, so I tried to figure out a rails set for one owner's hitch that she has - though she has no truck (Widow, long story).
There is no reasonable way to mount a (regular production) Reese - Drawtite turn-table over a flat bed and get to a workable pin height.
I looked at the various hitch adapters and converters, they all add too much height and/or require modification of the trailer - these are not MY trailers, so I'm not getting into that possibility.
Summary/Conclusion;
If you want a flat bed AND want to tow both goosenecks and mini 5th wheel trailers you will need to plan WAY ahead for this.
There is ONE hitch on the market that might do the job, but it is somewhere around $800, so I haven't investigated it to see what height it would end up at.
It might be worth it for someone who owns and uses both trailer types, but I don't.