I got a freebie pair of ST-6600 Ultegra Flight Deck shifters, but it was tagged "only shifts to big ring"- so I don't know if either Left or Right work, or how well.
I'd like to bench test them out without undoing the perfectly functional 9 speed set-up I have on the target bike, in case they need repair or are junk.
Is there an easy way, to just install a cable and tension it somehow, and actuate the shifter?

You can install cables and clamp them in a vise or have someone hold onto the ends whilst you click through the stops. A quicker way to see how they function is to simply run through the clicks. If you find one of them is sticky, try dousing the internals with WD-40 or other similar product. I have miraculously resurrected shifters using said method as have many, many users of this forum.
John
PS If you search for gummed up shifters or other similar terms, you will find lots of previous posts on the subject.

Yep, just run a cable through it, step on the end and pull on it lightly to give it some tension.

If it's listed as only going into the big ring, the factory grease has probably turned into peanut butter and is preventing the pawls from springing back into place, allowing the shifter to ratchet like it should. This also means you won't be able to run a cable through it as it needs to be in the position that would have it in the smallest ring, for both front and rear shifters.
9 speed STI's can't be disassembled very much so they're not as easy to clean as the earlier 8 speed shifters. Still, you can clean them. Last pair I cleaned, I cut down a one quart yogurt container to about half the height it was, filled it with diesel fuel (use whatever solvent you like), removed the rubber hood from the shifter, put on a pair of gloves and worked the shift levers to get the solvent to break down the old grease. If you want to let it soak, that wouldn't be a bad idea either. You could get some sort of sealable container (like a quart yogurt container), fill it with a good amount of solvent, drop it in, put the lid on and shake the dickens out of it. Then let it sit a while, rinse and repeat.

Yes - mount the lever on something to hold it steady, install an old (but not frayed) cable, and clamp both cable end and lever mount thing in a bench vise. Now you can apply firm tension to the cable with one hand while operating the lever with the other hand. If all the clicks are there and you can run up and down the gears reliably without the cable failing to latch then you could be onto a winner.
I would perform the usual flushing out with WD40 before testing, to improve your chances.

I suppose without a spare bike to fully install as a mock up, you want to avoid all the swapping of cables and such.
Even installing on a handlebar kicking around - while running the cables all the way thru - can take a good hour.
Worth considering if you foresee the need to replace cables. Yeah, run WD-40 into each shifter to see if it frees it up.

You want to secure them to something fairly solidly. Holding it it your hand, or something flimsy will make a simple one minute (if that) diagnosis a PITA. If you have a spare hbar and stem, use that, if not you can secure a dowel, broom handle or anything similar of the proper diameter on a vise. Don't forget CLICKS=SPEEDS-1, and the left shifter has trim clicks.

Most of the time, heating it up with a hair dryer, or leaving it out under a hot sun, will soften the grease enough to allow the brifter to shift back down to the bottom.

I had a shifter I didn't care about and a lighter and made quick work of it but I don't recommend this method as it is easy to screw up and potentially slightly dangerous but it was a free shifter and I was bored.

Honestly, you can test the shifter in your hand and without a cable just fine. If the shifter is balky, you’ll know it without the cable present. Pull the brake lever down a little and watch the mechanism that the cable moves on to see if it really moves.

I’ve tested hundreds of shifters to see if they are worth keeping. Never needed a cable to tell me one way of or the other.

Never thought of that, good idea.

I mounted up the brifters on an old handlebar and found an old shifter cable in the bin, so my test setup was fine.
With copious WD-40 and a heat gun, I got the LH shifter working, though still a little crunchier than I'd like.

The RH is still problematic, despite coming close to overheating it and melting things. I put PB Blaster in it to sit overnight.

For gummed up brifters, Barnett's Bicycle Manual recommends disassembly and soaking in solvent. I found an easier way.

I used a product called CRC PowerLube. Solvent with PTFE (teflon) so it lubes the internals as the solvent dissolves the gunk.

I'd direct the spray into the shifter, work the shifter both ways, and repeat.

Completely freeing the shifter usually took anywhere from a minute or two to 10-15 min, depending on how gummed up it was.

Shifters treated with PowerLube seemed to shift more smoothly than the original lube. Go figure.

You don't need to install the shifters anywhere, as long as the initial stretch of the cable (from shifter to the first frame boss) is covered by cable housing. All you need to do to make a representative test is to install a piece of housing from the shifter to the frame (can be shorter than usual), and then route the cable all the way to the derailleur(s) the usual way. Whether the shifter itself is installed somewhere or hangs freely has no impact on its operation.

On further disassembly, it turns out gunked up grease is not the problem, but wear. The "b" (small) shift lever, at full stroke, does not lift the ratchet lever quite high enough for the index to trip. If I help it with a screwdriver blade it kicks over. Oh well, at least I have a spare working LH shifter.