So the doldrums can refer to a deadish wind pattern around the equator, or an emotional state of being vaguely depressed.
Which one came first and named the other?
The emotional state came first, though it was often used to indicate that someone was dull or stupid and not necessarily depressed. Online resources vary a bit, but most say that the word likely comes from either dull, dulled, or the Middle English dold (evolved into dolt).
One site said that it might have been pattern matching, combining dull with the last half of tantrum (sorta, d instead of t, but you get the point).
The first use is usually given as somewhere in the late 1700s, with some sources saying as early as 1765 and others as late as 1795. Sources generally agree it was in common use by 1805 or so.
The application to wind patterns and sailing ships started in about 1820 and gained popularity between 1820 and 1850.
Wow, thanks ECG, you’ve answered my question in one!