What is the weapon attack damage of a tentacle rod?

The tentacle rod’s description includes the following (emphasis added):

Made by the drow, this rod is a magic weapon that ends in three rubbery tentacles. While holding the rod, you can use an action to direct each tentacle to attack a creature you can see within 15 feet of you. Each tentacle makes a melee attack roll with a +9 bonus. On a hit, the tentacle deals 1d6 bludgeoning damage.

Answering this recent question, I concluded that the three attack feature of the tentacle rod is incompatible with extra attacks. In this older question, it was concluded that it is also incompatible with opportunity attacks.

However, I was then wondering, how making a normal weapon attack would work with the tentacle rod (without the three attacks property). This is clearly possible and in the case of the opportunity attack it can very well be worthwhile if you do not have better plans for your reaction. Usually, magic weapons have the respective item category (e.g. the scimitar of speed, which says "weapon (scimitar)") which defines a weapon damage in that those weapon types are detailed in the PHB (p. 149).

The description clearly states that the rod is a weapon (vide infra), its category, however, is rod. The magic item categories (DMG pp. 139-140) state that a magic staff can be used as a quarterstaff unless stated otherwise, while a rod is "A scepter or just a heavy cylinder". This was confirmed in this question about rod of the pact keeper.

It seems therefore, that the tentacle rod is a weapon by RAW but has no weapon type or weapon damage defined.

The rules on improvised weapons (PHB pp. 147-148) state:

An improvised weapon includes any weapon you can wield in one or two hands, such as broken glass , a table leg, a wagon wheel, or a dead goblin. Often an improvised is similar to an actual weapon an can be treated as such. For example, a table leg is akin to a club.

It further states:

An object that bears no resemblence to a weapon deals 1d4 damage (the DM assigns a damage type appropriate to the object).

Now the last part should not apply because the rod clearly is a weapon. I can simply decide what weapon the rod is like (probably a quarterstaff, club, or a whip). I am wondering, however:

Is there anything more clear on the subject, either additional rules on improvised weapons, or specific information on the tentacle rod, that would give guidance on the matter?