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Can I use an 11spd Shimano 105 R7000 Rear Derailleur with 10spd shifters and cassette
No
But maybe a 9spd MTB RD would work with 10spd road shifters?
It will.
Would the newer style "shadow cage" 9-spd RDs work?
Yes.
Is it only road RD that 10 and 11 spd shift-activation ratio differs?
Yes, 10 and 11 speed MTB shifters have the same cable pull per click. That's why 11 speed MTB rear derailleurs are sold as 10/11 speed.
Can I use an 11spd Shimano 105 R7000 Rear Derailleur (https://www.probikekit.co.uk/bicycle-derailleurs/shimano-105-r7000-rear-derailleur/11746883.html) with 10spd shifters and cassette or is there some ratio difference that will mess things up?
If this won't work, what's a similar long-cage RD that will work with 10spd cable shifters?
"Forget about using Dura-Ace 7900 derailleurs with 11-speed levers. The derailleur’s shift-activation ratio is different for Shimano 11-speed rear derailleurs than it is for Shimano 10-speed rear derailleurs. Furthermore, Shimano 10-speed mountain and road rear derailleurs have different actuation ratios from each other, and the same goes for Shimano 11-speed mountain and road rear derailleurs. Prior to road 11-speed and mountain 10-speed, things were simpler; Shimano road rear derailleurs up through 10-speed and mountain-bike rear derailleurs through 9-speed all have the same activation ratio."
https://www.velonews.com/gear/technical-faq-10-11-speed-drivetrain-component-compatibility/
Sounds like a "no".
But maybe a 9spd MTB RD would work with 10spd road shifters?
https://www.youtube.com/watch?v=2Q61siPOo_w