Turns out the fuse was blown. I don't know how I didn't see it the first time. Unfortunately, the new fuse lasted all of 8 seconds. I have no idea how to chase down something like this.

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63 220S W111
76 300D W115
2013 VW JSW TDI M6

previously-
73 280 SEL 4.5
86 300E 5 speed
2010 VW Jetta TDI M6