Bongo Bongo is interesting in that it did have a little bit of a story behind it. It was originally sealed in the shadow temple but Impa years before the time of the game. And was released by Ganondorf after he took over Hyrule and secured the temples. It is referred to as a shadow spirit by Sheik when Link returns seven years later.
Link....A terrible thing has happened! The evil shadow spirit has been released! Impa, the leader of Kakariko Village, had sealed the evil shadow spirit in the bottom of the well.... But the force of the evil spirit got so strong, the seal of the well broke, and it escaped into the world!! I believe Impa has gone to the Shadow Temple to seal it again, but...she will be in danger without any help!
An old man in Kakariko tells the story of the man who could see the truth and that his house was standing where the well is now.
A long time ago... There was a man in this very village who had an eye they said could see the truth! Now usually, you have to train your mind's eye most strenuously to actually see the truth... But this fella, no, they say he had a different way of doing things... His house stood where the well is now..
Possibly creating some kind of connection between the two as the lens is needed to pass the Shadow Temple and see Bongo Bongo. And that the area at the bottom of the well looks like an extension of the Shadow Temple.
It is clearly some form of spirit as Link requires the lens of truth to see it, like all other ghosts and spirits in the game. The Shadow temple itself is very similar to the Arbiter's grounds in that it appears to be a prison of some kind that is no longer in use. The inscription on one of the main doors reads
Here is gathered Hyrule's bloody history of greed and hatred
Either referring to the lawless individuals imprisoned there or that it tells the bloody history of Hyrule and many people suffered there in the name of the crown. There are many jail cells inhabited by redeads, torture devices, and bombable walls made of skulls and bones. It has a lot of death symbolism within it as well, with the many blue fires throughout, the large skull statues, and the twin grim reaper trap near the beginning. It also has a ferry that takes Link over a smoky ghost like river to the end of the dungeon, possibly meant to symbolize the mythological Charon's ferry that carried spirits to the land of the dead in Greek Mythology.
This could lead me to think Bongo Bongo could be one of three things. A great and terrible shadow demon attracted to the death and suffering of the Shadow Temple Prison and continues to haunt the area. The restless spirit of a criminal that was taken there and died. His severed hands show that he might have been punished for theft or other such offense. Or a massive accumulation of the emotions of hatred, suffering, greed, and agony created it and it resembles a mix mash of evil spirits in the forms of punished souls. This might explain why both hands were severed instead of simply one as would be the punishment for theft. And why it was hanging from the ceiling as hanging from the feet was a common form of punishment as well.
Why it beats a drum might be largely symbolic. Drums have long been important tools of shamans to communicate with the spirits and strange rituals that summon it might have used large drums that it used in the fight with Link. That might be the very drum that summoned it in the room.
The drum is used by shamans of several peoples in Siberia, the Inuit, and many other cultures all over the world, although its usage for shamanistic seances may be lacking among the Inuit of Canada. The beating of the drum allows the shaman to achieve an altered state of consciousness or to travel on a journey between the physical and spiritual worlds. Much fascination surrounds the role that the acoustics of the drum play to the shaman.
http://en.wikipedia.org/wiki/Shamanism#Music.2C_songs
The large magic circle and altar in the entrance of the dungeon hints at shamanistic rituals taking place in the Temple as well. Many cultures did have some form of ritualistic sacrifice of prisoners.
Another interesting thing about the temple is the Gerudo Symbol that appears in one area on a turning puzzle meant to open a door.
And again on a movable block
So much like the Arbiter's grounds it appears to be a former prison filled with the restless spirits of criminals, and it has a connection to the Gerudo. The builders of the Spirit Temple. It is interesting to me that a Spirit Temple and a Shadow Temple, filled with restless spirits could have been built by the same people. Or that Gerudo could have been imprisoned here as well during the warring period of Hyrule's History.
Another possibility is that Bongo Bongo was a larger more powerful Twili Shadow Beast. It bears a few similarities in that it has a single eye for a head surrounded by large tendrils. While the Common Twili Shadow beasts have a type of shield or armor with a single round design, possibly representing an eye, surrounded by many smaller tendrils. Both have shadowy powers in that they can melt into shadows and move as if they were spirits. Midna says in TP that the twilight turns mortals into spirits, as it sis for the Hylians of Castle Town, so they would have very spirit like abilities such as intangibility and the ability to be invisible or move through shadows.
The common Hylians of OoT time might not know of the Twili at all, but only think of it as some form of shadow based creature and sealed it in Kakariko well. However Impa, being a Sheikah and confidant of the Royal Family, might know exactly what it is and would know how to fight it. Haunting a shadow temple would not be too odd for the creature since the Twili, before being sealed in the twili realm, were masters of shadow magic and might have very well built the Shadow Temple in the first place.