Remapping Caps Lock with xmodmap doesn't work

The xmodmap(1) man page has an example for exactly this

   !
   ! Swap Caps_Lock and Control_L
   !
   remove Lock = Caps_Lock
   remove Control = Control_L
   keysym Control_L = Caps_Lock
   keysym Caps_Lock = Control_L
   add Lock = Caps_Lock
   add Control = Control_L

but if you want to finish doing it the way you started, I think you need to add at least the remove and add lines

   remove Lock = Caps_Lock
   remove Control = Control_L
   keycode 37 = Caps_Lock
   keycode 66 = Control_L
   add Lock = Caps_Lock
   add Control = Control_L

I'm guessing that's the case based on this paragraph

   add MODIFIERNAME = KEYSYMNAME ...
           This adds all keys containing the given keysyms  to  the  indi‐
           cated  modifier  map.  The keysym names are evaluated after all
           input expressions are read to make it easy to write expressions
           to swap keys (see the EXAMPLES section).

which makes it sound like modifier changes (shift, control, etc.) don't get applied until you run that too.

(And logically the same with remove)

The keycode version has the advantage of being idempotent, meaning that the effect won't change if xmodmap is run multiple times.

Loosely related answer: I wanted to remap the caps lock key to left control, leaving the actual left control untouched. The xmodmap man page also offers the solution:

    keycode 66 = Control_L
    clear Lock
    add Control = Control_L