What does the phrase "a mouth by gum have I" mean?

I came across this song by Frank Sinatra "Pass Me By", with the following lyrics:

I got me ten fine toes to wiggle in the sand,
Lots of idle fingers snap to my command,
A loverly pair of heels that kick to beat the band,
Contemplating nature can be fascinating,
Add to these a nose that I can thumb, and a mouth by gum have I
So tell the whole wide world, if you don't happen to like it,
Deal me out, thank you kindly, pass me by.

It puzzled me what exactly does 'a mouth by gum have I" mean? and How does the grammar work for that phrase?

here is the link if it helps:

https://www.youtube.com/watch?v=vB2bkEOeVq0

"By gum" is an old-fashioned term originating in the UK and wandering across the pond. It is generally defined as a term of surprise, but it is also used as emphatic assertion. With respect to the grammar, it's fair to say that Frank was probably more interested in meter and rhyme. He might have written "I've got a mouth, by gum," but the song probably wouldn't have sold as many records.