I define a function:
func3[a_,OptionsPattern[$opt1->False]]:=Module[{junk}, Print[OptionValue[$opt1]]]
It works as expected when invoked as:
func3["abc",$opt1->True]
But, if I type: Options[func3] I get '{}' as the response rather than (as I expected) '{$opt1->False}'
If I type: Options[Plot] or any other system function
I get the options for the system function. The docs for Options don't mention any restrictions the function specified. But, I can't get it to work for any of my (user) functions.