Calfee Tetra Tandem new October 2012 with 10 speed setup. Bike has 3500 miles ridden to date. This is a top of line road tandem.

Bike equipped with:

Dura Ace brifters St 7803 (old style with cable not under tape)
Two different rear derailleurs: XTR RD M972 and Ultegra RD670. Right now using the 670.
Dura Ace chain

The rear has never shifted right from get go. The problem occurs on 2 of the middle cogs on the cassette. When shifting to a bigger cog in the middle of the cassette it requires 2 clicks of the shifter instead of one as with the other cogs. Going the opposite way to the smaller cog it will jump a cog at the same point on the cassette. (It doesn’t do this every time, but most every time.) It has been adjusted by 2 different mechanics that I trust on multiple occasions without improvement. The last go around it has a new derailluer, cable and chain. The hanger was checked and found dead on.
The last possibility seems to be the shifter. Mechanic did spray the shifter to clean it out. It’s an expensive proposition to swap the brifter out. Any thoughts?

Is the cable run too short or the housing bends too tight, particularly the housing section from the chainstay to the derailleur itself? Is the housing in good condition and the cable not frayed?

I bet the cable is hanging up at that point of its travel. I would replace the cable, and remove and inspect the ends of the housing to verify there are no burrs or restrictions in the cable's movement.

"I would replace the cable, and remove and inspect the ends of the housing to verify there are no burrs or restrictions in the cable's movement."

Might as well replace the housing, too, while everything is apart. Make sure that the housing ends are properly prepared; ground or filed flat, with the inner lining reamed open and no stray wire strands protruding and fitted with the appropriate ferrules.

Ok, so what's left - cassette and shifters, and cable lenght / tension. Any reason why the mech's won't try new cassette and shifters in the shop to see if that fixes it? Doesn't make sense to put on new components that are not fixing it and have soak up the cost for nothing. Oh, did the cable housing get replaced along with the cable and is it routed correctly? Jeff and Hillrider may be spot on.

Cable run in NOT too short. Cable and housing and casette have all been replaced.

Is this possibly one of the "off brand" cassettes?

This happens on my SR. it's because i've married brifters to an RD that was made well before brifters and i've slapped a different range freewheel on to the wheel. i get gear jumps. i can compensate, occasionally, by holding the shift a little longer than usual and not shifting as far. this is when i'm down shifting for climbs or slowing, or even coming to a stop. i find the jumps into higher gears occur when i'm not pushing a full load onto the pedals. if i increase the tension while sprinting the shifts are usually more precise, but not always. again, this is an older setup with all original 105 drivetrain save for my shift levers and freewheel. no amount of tuning or cable replacement has changed any of this. not sure about current Shimano tech, but i do have some trim in both levers, which i guess is more the result of using older slave mechs with the later STI's.

My two cents, maybe some of this mirrors your situation. good luck!

Is the cassette lockring tight? Possibly some dirt trapped between the cog spacers or mismatched/damaged cogs in the cogset. Are you using one of the 7900 DA chains with the cutouts on the sideplates as these need to be installed for one direction and may hurt the shifting if reversed.

Have you had the derailleur hanger alignment checked?

If not, I'd do it. If for no other reason It would be nice to eliminate that as a possible source of the problem.

Cassette is Ulterga

"Have you had the derailleur hanger alignment checked?"

Did you read the entire post? Alignment has been checked.

One thing you did not mention was the cable housing. Has it been removed and inspected from front to back? You're describing symptoms of binding or resistance in the cable, so you need to verify that the cable runs freely in the housing at all points along the cable run. Since it's not the cable, you need to check (or simply replace) the housing.

Long ways between command at the front, and action at the rear ..

Update? what have you tried already?

you ask:
Any? well I love the self-contained nature of a Rohloff hub, all the index sequencing is in the hub.

so a long cable run is not altering the shifting lag significantly.

not much help , I know, buut a thought to share nonetheless..

Your, having gone down the derailleur path, how about an electronic Di2 shifter conversion ?,
to eliminate the mechaanical lag of the cable entirely.