Joy! When I pulled off the module, I found the connector partially detached, possibly from when I cleaned out the firewall debris a few weeks ago. I pushed it back in and the idle dropped back to normal. If the problem comes back I'll know to check here for bad solder joints too.

As always, thanks to all who responded.

FYI, the idle module is also called the Leerlaufdrehdahlregelung (!)

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1985 380SE Blue/Blue - 230,000 miles
2012 Subaru Forester 5-speed
2005 Toyota Sienna
2004 Chrysler Sebring convertible
1999 Toyota Tacoma