Green’s Dictionary of Slang

brown nose n.

also brown snout
[brown-nose v.]
[1930s+]

1. (orig. US milit.) a toady, a sycophant.

2. attrib. use of sense 1.

In phrases

have a brown nose (v.)

[1960s+] to be a sycophant.

one’s nose is always brown

[1930s+] said of a dedicated sycophant.