6-speed road STI levers have never been made.
There were some 6-speed road freewheel hubs spaced narrower than the standard 126mm, but they also use narrower sprocket spacing than a standard six. The Suntour Ultra Six, for example, used 5mm (7-speed) spacing and fit a 120mm frame. They're rare these days, and if this is a bike you plan to use, it doesn't make a lot of sense to run it on rare consumables.
You do have a few options, depending how creative you want to be.
You can run friction bar-end shifters and a 5-speed block, as the bike would have been used originally. 5-speed freewheels are around, new, and probably will be for a while.
You could run a 'Shimpagnolo' combination. Older 9-speed Campag levers, a Shimano mech, and a 5-speed freewheel should work:
Some 7-speed freewheels use a pair of threaded, overhanging sprockets in the 1 and 2 positions. Replace them with a single sprocket, and you have a narrow-spaced 6. This will take some homework to find out what will work and get a supply of parts, but you should be able to get it to fit your frame.
You could get creative with the hub. Hubs have been made with short cassette bodies - for trials use, for special applications like Moultons and the newish Shimano Capreo. Phil Wood made a series of hubs with special, short cassette bodies. You might be able to adapt something to fit into your dropouts. You can then use separate 9-speed cassette sprockets to build a narrow cassette to fit the hub, and use modern indexing parts to shift it. Again, this will take some research (and probably some time trawling eBay) to get a working system together.
You could fit a fixed hub, or a BMX freewheel or cassette hub, or a hub gear, as I suggested last time you were asking. That's probably the simplest solution, but means a single gear (or a reduced range of gears). You can actually cram three sprockets on a Shimano DX BMX freehub...
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De ce silence profond.