how to create a function in plpgsql which picks the name of a variable which is NULL out of a list of variables?

Hello. I am trying to create a function in plpgsql, but I got stuck on
one issue, looking for some clues.

Inside the function I have 4 variables of type boolean:

a1 boolean;
a2 boolean;
a3 boolean;
a4 boolean;

Their values can be TRUE, FALSE or NULL;

Now I need this function to return the name of a randomly picked
NULL-valued variable out of these four, or return NULL in case none of
the 4 variables are NULL.

So if for example a1 is TRUE, a2 and a3 are NULL and a4 is FALSE, then
the function should return string 'a2' or 'a3' (randomly picked).

I written this part, but looking for any clues how to proceed:

CREATE OR REPLACE FUNCTION pick_random_a(thisid integer) RETURNS varchar(2) AS $BODY$
DECLARE
a1 boolean;
a2 boolean;
a3 boolean;
a4 boolean;
this_a varchar(2);
BEGIN
SELECT va1, va2, va3, va4 INTO a1, a2, a3, a4 FROM tmp_a WHERE id = thisid;

--
-- so here should be some block which gives the variable this_a
-- a string or NULL value, how to do it?
--

RETURN this_a;
END;
$BODY$ LANGUAGE plpgsql;

--
Miernik
http://miernik.name/