Now, regarding the tail lift as being negative or positive, I had the notion that it had to be always negative because of the aerodynamic moment, and that a tailplane was necessary (an then the germans invented the flying wing)
Hmmm ... but on a certain very fast tailless aircraft the wing/body cp and cruise CG (with fuel transfer) were arranged so that the elevons were deflected slightly TE down (positive lift) to keep the drag down.
But what I think is just that for the airplane to be in trim, the tailplane lift has to able to balance all the other pitching moments, whichever they are. These are basically those due to the wing plus fuselage lift at the wing-fuselage cp, the thrust and the drag.
The Drag-Thrust couple usually gives a nose up (positive?) moment, and the Lift gives a nose down (negative?). The tail lift has to balance the resultant of those moments. I guess that the Lift effect is much greater than the T-D couple? It seems so if Lift is many times bigger than Trust for Drag, but it depends on where the wing-fuselage cp lies. I deem it does lie well aft of the CG?. That would be why the tailplane has to produce a pitch up (positive?) moment with negative lift. But can the cp be ahead of the CG for "normal" angles of attack?
Maybe if we put in some numbers? these are not specific to any one type, but they are realistic.
Modern airliner wings have the section (camber and thickness distributions) and twist (local AoA variations) carefully tailored to maximise performance (NOT to minimise drag since wing loads/weight come into the equation). In addition their planform is usually swept and has a compound taper. Consequently it is very difficult to pick a 'real' chord to represent things and it is usual to calculate a 'mean aerodynamic chord' (mac or amc) based on planform and use that as a reference 'axis'.
The wing body CP in cruise conditions varies between 30~40% mac depending on lift coefficient and Mach number, with the higher end corresponding to the maximum cruise Mach (Mmo). If you back off to best economic cruise conditions then the CP will be around 35% mac.
On an aircraft without fuel tanks in the tail the CG limits will range from 15~20% mac at the forward end to about 30~35% mac aft. If the aircraft has a tail tank then the aft limit will stretch to 40% mac, maybe a touch more.
Just glancing at those values you can see that in most cases the CP will be behind the CG and you will need negative tail lift to trim, but if you have and use the tail fuel tank then the CG can be at or behind the wing/body CP and the tail lift will be either very small or positive. Factor in the nose-up pitch from the drag/thrust couple and you will definitely have positive tail lift to trim.
Just to round things off, the complete aircraft (tail on) aerodynamic centre will be around 50~55% mac so the aircraft would be stable even at the aft CG limit (as it must be of course to meet regulations)