I've copied your code and compiled it but find that the resulting program isn't transparent. It is borderless and immovable but 'grey'.
Maybe you didn't connect the FormCreate-event to the form.
That's certainly a posibility.
Anyway... attached is the same unit but in a working project. See if that works (although like I said the component/button is also click-through so doesn't work).
Yes - that works and yes the button doesn't

Yes, the ability to interact with the components on my form (though they will be few) is imperative.
Ok, in that case you really need to go for a variable shaped form. Could you say something about the form of the component you have on your form. Can is be drawn with one line (be it not rectangle).
There would only be an active button to close the project - closing via the Task Manager should not be considered a default state! I haven't yet figured out how to make a program [start] automatically so there might need to be a start button as well. Other than that, there would be Tlabels to display Day, Date, Moon phase - possibly Easter, Vernal and Autumnal Eqiunox
I'll look into creating a non-rectangle form in Lazarus tomorrow.
I see you have already posted a procedure (I've not had time to investigate it yet) to create an elliptical region - how did you guess that the ellipse is my favourite mathematical figure !!
It never occurred to me that anything other than a rectangular form (OK square as well) was even possible.
User 137's suggestion of four forms looks promising but it would actually have to be 5 forms - 4 around the screen edge and one to hold the Day, Date etc. that I've just described and that needn't be transparent, it could be border-less and positioned anywhere I wished. Being border-less would be less important so could just as easily be a 'normal' form with the usual controls.