[General] undertaker of a man-servant

[luxury20041985]

A: I was hoping you would come to me last night.
B: I was tired.
A: Your exertions below deck would have no doubt exhausted you.
B: I see that you sent your undertaker of a man-servant to follow me around, how typical.
Titanic (Film)

How can I interpret “undertaker” here? Saying "sent your man-servant" would suffice. How does "undertaker" contribute meaning to the sentence ?

 

[Tarheel]

It's hard to say, but it could be a comment on that individual. (The person's personality, for example.)

 

[Tdol]

They might look like an undertaker- wearing sombre clothes and looking serious.

 

[Rover_KE]

An undertaker is a funeral director, such as our local guy, Phil Graves—often having a professionally solemn demeanour.

In this context, A's manservant must have resembled one such.