Bought a 427 Vette with 3 deuces.
I don't think the 1st and third carbs are operating. Linkage does not move throttle plates. Are they operated by Vacuum?
Can the linkage be moved to the lower end of the cam on middle carb sot the 3 run progressive?

Yes, my recollection is that the front and back carb ARE vaccuum operated. The motor normally would run off the middle carb. You could possibly get progressive linkage but since the carbs were not designed to work in this fashion, the motor would run very poorly because of the lack of accelerator pumps on the vaccum operated carbs. What you would experience would be bogging. You CAN change out the springs that control the opening of the vaccum carbs with WEAKER ones which would allow the carbs to open sooner.

sr71bb has it exactly right if the front and back carb are working right you won't feel anything it will just keep pulling. The diaphrams do break make sure they work.

The tri-power Vette carbs are vacuum secondary just like the later Chrysler 440 Six Pack. You should find that you can hold the primary ( center carb ) open and move the secondary carbs open by pressing up on the diaphram shafts on the passenger side of the carbs ( I hope there are daiphrams on the outboard carbs ). There were a lot of junk mechanical conversions sold for this set-up in the late60s and early 70s. The job of the factory mechaniical linkage is to close the outboard carbs only! You should have a tee with rubber vacuum lines on the passengers side of the center carbs metering block going to both outboard daiphram housings. You can check the condition of the rubber diaphrams by removing the housings depressing the diaphrams and blocking the air bleeds and vacuum line fitting and seeing if the diaphram shafts stay up against the return springs under the housing covers ( I believe that Holley still services these parts but they were very expensive. I would buy a pair of replacements and keep them in a sealed sandwich bag as they rot over time when exposed to atmosphere ). You cannot just block the vacuum line going to the carbs beacause there are internal bleed passages from the housing to the carbs venturri.