In this older question, it was concluded that it is also incompatible with opportunity attacks.

Rods, contrary to staffs, cannot usually be used as quarterstaffs (see this question about rod of the pact keeper ).

Often, an improvised weapon is similar to an actual weapon and can be treated as such.

I can simply decide what weapon the rod is like (probably a quarterstaff, club, or a whip).

That, to me, speaks to weapon being used correctly in the description here, not as very-poorly-chosen descriptor.

It may not matter, but if for any reason you are better with clubs or light maces than you are with some random improvised weapon, Id let you have it.

However even though it uses the word weapon it does not make it eligible for say, extra attack, or spells which affect weapons.

As such it is 100 in the DMs judgement as to allow it to be treated as an existing weapon.

Provide details and share your research But avoid Asking for help, clarification, or responding to other answers.

Making statements based on opinion; back them up with references or personal experience.

MathJax reference.

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5E Dmg Magic Iturments