KAKEKOTOBA ( Paronomasia ) is one of the most important
literary devices in Japanese classical poetry. In the above poem,
a noun NAGAME ( a long rain ) and a verb NAGAMERU ( to be lost
in deep thought looking out aimlessly ) are used for this purpose.
This perticular combination was very popular and used in countless
occasions by countless poets.
Let me cite a  few more examples: MATSU ( pine tree, to wait ),
FURU ( to rain, to pass-as in time ), AKI ( autumn, to get tired of ),
YORU ( night, to come closer ). KARERU ( to whither, to leave ).
There are other literary devices such as JOKOTOBA or JOSHI
( forewords ), ENGO ( associate words ), MAKURA-KOTOBA
( pillow words ). I'll try to explain them later.

These may seem nothing but whimsical plays of words but when used
properly, I would say, they are very effective.