If I do
M-x apropos RET cursor RET
I can see the variable `cursor-type', but if I do
M-x apropos-variable RET cursor RET
I can not find it in the list shown. To me that is at least a bit
surprising. Should it be that way?
Yes, according to the doc:
Show user variables that match pattern.
...
With C-u prefix, or if `apropos-do-all' is non-nil, also show
normal variables.
I suggested that this command be renamed `apropos-option', for this very
reason.
I do this in my own code, and add an `apropos-variable' that does the same
thing, but with `apropos-do-all' bound to t. Clearer, IMO.