Cfrtjryk

I can stare at the sun from dawn until dusk,

on the famous flat mount where you may smell my musk.



And if I should smile, you may see my tusk;

like my long-nozzled uncle who's big, brash and brusque.

What am I?

I think this peculiar creature is a

rock hyrax

I can stare at the sun from dawn until dusk,

Hyraxes are primitive animals, exhibiting many traits characteristic of early mammals. They are weak at internally regulating their temperatures, and are often seen basking in the sun.

on the famous flat mount where you may smell my musk.

Found on Table Mountain, they have a dorsal gland, which secretes an odour marking rocks.

And if I should smile, you may see my tusk,

The rock hyrax has a pair of long, pointed, tusk-like incisors.

Like my long-nozzled uncle who's big, brash and brusque.

Along with other hyrax species and the manatee, this species is closely related to the elephant.

Are you

A sea lion?

I can stare at the sun from dawn until dusk

sea Lions are known for basking in the sun by looking upward: https://binged.it/2KByZjn

On the famous flat mount where you may smell my musk.

Not sure about the exact mount referenced here, but sea lions like flat areas and anyone who's been to Pier 39 in San Francisco can attest to the musk

And if I should smile, you may see my tusk;
like my long-nozzled uncle who's big, brash and brusque.

Referring to the larger, toothier, walrus

Are you

Elephant Trunk Hill, which is adorned by a tower that is a tourist attraction and therefore a famous mount? You would also have a trompe-l'œil of the moon appearing below your trunk and looking like a tusk or a smile, but only at times that are not between dawn and dusk. And you have a larger uncle in the form of Xiangshan, the Elephant Mountain.

Not sure about your musk. . .