The Immovable Rod says:
You can use an action to press the button
(DMG, p175.)
An humunculus "is a construct that acts as an extension of its creator".
Can your humunculus push the darned button on your Immovable Rod?
The Immovable Rod says:
You can use an action to press the button
(DMG, p175.)
An humunculus "is a construct that acts as an extension of its creator".
Can your humunculus push the darned button on your Immovable Rod?
Immovable Rod
Until you or another creature uses an action to push the button again, the rod doesn’t move, even if it is defying gravity.
The Homunculus has a stat block (S 4/D 15/C 11/I 10/W 10/Ch 7). As a construct, it is a creature. It can interact with things. (Example: with it's bite it makes a melee weapon attack).
There is no minimum strength required to push the button listed for the item. I see no reason to argue that it can't push the button.
As I read the introduction to "Monsters" in the rules, all monsters are creatures. That makes constructs a kind of creature.
(MM p. 6) Constructs are made, not born. {snip} Many creatures native to the outer plane of Mechanus, such as modrons, are constructs shaped from the raw material of the plane by the will of more powerful creatures.
Here's an image of a possibly typical homunculus:
As you can see, it generally has normal appendages, and is physically capable of interacting with things, and the Immovable Rod has no special requirements about being able to use it (i.e. you don't need a Use Magic Item check to press the button). So, under normal circumstances, your homunculus should definitely be able to activate immovable rods without any difficulty.