Long bed TC on short bed truck

How long are you talking? If it is an 8 ft, it would obviously be better than a 11 1/2.

I did it with 12' camper, but the shortbed was a flatbed who was actually 7' long.
With strong tailgate and camper no longer than 10' I would not see structural issues.
COG might be another story and after driving on scales with the combo, I start shopping for dually next week.

used one with the tail gate down for years no ill effects

Couple very important things.

One the tie down points (where the TC anchors are in relationship to the truck mount points will be askew and you won't be able to secure the camper properly..

Two, your horizontal center of gravity will be too far rearward, putting an excessive amount of load on the rear axle and most likely causing very adverse handling

Three, the camper itself might not be structurally rigid enough to take the strain of half of it hanging out the back, unsupported.

I'd advise against even considering it. It's not safe to do. Why campers are built for specific bed lengths in the first place.

It is possible to put a short bed TC in a long bed truck (Northstar offers their pop up line as such), but not the other way around.

Unless it is a TC from the mfgr that can be mounted to either a SB or LB truck then there could very well be COG issues.

...my bet would be that a strictly LB camper generally will not work on a SB truck.