Which gland plays a very important role in the regulation of the $24$-hour (diurnal) rhythm of our body?

Identify the correct gland on the basis of the following characteristics:
$(I)$ It is located on the dorsal side of the forebrain.
$(II)$ It plays a very important role in the regulation of the $24$-hour rhythm of our body.
$(III)$ It helps in maintaining body temperature.
$(IV)$ Its hormone influences metabolism as well as defense capability.

Melatonin is secreted by the . . . . . . .

Which of the following endocrine glands acts as a biological clock and a neurosecretory transducer?

$I.$ Sleep-wake cycle, $II.$ Body temperature, $III.$ Pigmentation, $IV.$ Metabolism, $V.$ Defense capability. All of the above-written activities are influenced/regulated by:

The organ which was considered vestigial until recently but is now confirmed to be an endocrine gland is: