Because of this thread, I revisited to my inoperable cruise amp and attempted one last fix.
I employed my newly acquired heat gun (which has been so useful, I've considered using it in the kitchen) and attempted to reflow the solder.

I didn't reflow much solder but I did cook the thing to near smoke point and I'll be damned.

I now have working cruise control.

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1981 240D 4sp manual. Ivory White.