OK, so according to Larry Pina's Classic Mac Repair book, this is the 'Linearity Coil'.
They don't seem easy to come by, I assume because they are only needed for CRTs: https://newly.en.ec21.com/Horizontal_Linear_Inductor_Coils--1949388_1949720.html
I will probably solder the one I removed back on...
Switching to Cable Select enabled me to boot to an OS 9 CD and I could see the SSD partitions on the desktop. Installed OS 9 on the first partition, but the iMac refuses to boot from the SSD. Flashing folder w question mark - until a CD is inserted. Drives show up On desktop sometimes, not always.
Almost certainly a rotten trace in the soft power circuit. Look up the Macintosh II power circuit via Google: it is well documented, and many good illustrations are available to help you backtrack and buzz out the traces. They were probably eaten by electrolyte. Much of that circuit runs through the areas that you indicated with your red arrows in previous photos.