Turns out the trouble was in the fuse box. The red/yellow wire going to the blower regulator had a fusible link in it which was open and the wire on both sides of it, while not burned, were well cooked. We cut out the link, along with the cooked wire and patched in a fuse holder with a 40 amp fuse. It now works perfectly.

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2000 Mercedes S500
1990 Mercedes 560SEL
1970 Triumph Spitfire