That sounds right... that the RD is getting a continuous shift message from something. And, the something is most likely the source switch.

I would start with just blasting the crap out of the shifter with spray contact cleaner. Disconnect the battery first, and then just empty a bottle of the stuff up in there. Work the shifter while you are spraying. Look for a contact cleaner designed for electronics that dries with no residue. If that does not work, then you are heading toward a disassembly.

Why? - waste of time and money - even if it works now, it’ll stop working pretty soon again
Just order a new shifter, if it works toss the old one, if it doesn’t return the new one and write shimano again

It probably *is* a stuck switch, and it likely isn't all that difficult to fix if so. Page 87 of this document has an outline of the disassembly process. You will want to disassemble the switch unit, de-gunk, grease the springs, and reassemble.

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Tech writer/support on this here site. FIST school instructor and certified bike fitter. Formerly at Diamondback Bikes, LeMond Fitness, FSA, TiCycles, etc.
Coaching and bike fit - http://source-e.net/ Cyclocross blog - https://crosssports.net/ BJJ instruction - https://ballardbjj.com/

found the same gen shifters, NIB, for $130. Tried the contact cleaner but it just made the paddle worse. I'm not about to disassemble the shifter. This bike will just stay on the Kickr/Zwift erg mode until the new shifters arrive.

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"Outwork your talent." Kevin McHale