Here is one source I can find after a quick search: idioms.thefreedictionary.com
not know whether one is coming or going
Fig. to be very confused.
- I'm so busy that I don't know if I'm coming or going.
- You look as if you don't know whether you're coming or going.
That would fit with the songs:
The last example is telling:
You've got me on the road
Runnin' to and fro
Lookin' high and low
I don't know if I'm coming or going
Since I fell for you
I run up across the town
Chasing up and down
Having you around
I don't know if I'm coming or going
Since I fell for you
You certainly did your research!
Two crucial points that it's not clear if you came across, though:
1) SNL is an abbreviation for Saturday Night Live, a popular comedy show that features comedic stand-up skits and musical guests.
2) The cowbell, in addition to being a countable noun, is also an instrument.
Now, let's take a break and watch an excerpt from the skit in question.
The skit is a reenactment and parody of the studio recording of the song "(Don't Fear) The Reaper" by the band Blue Öyster Cult. The guy screaming "I gotta have more cowbell" is the producer. Because the cowbell player (Will Ferrell) and the producer (Christopher Walken) are popular actors, and because SNL was a successful show at the time, this skit became a big hit. The humor lies in that "more cowbell" seems like an absurd request - a background instrument becomes louder than the vocals, the melody, etc.
The phrase is "more cowbell" and not "more cowbells" because Walken is asking that the one cowbell that's there be played more loudly. This is actually standard usage - someone might similarly ask for "more bass" or "more guitar", both in the singular. (Or, in another context, someone might stay a stew needs "more carrot".)
The "more cowbell" joke can now be seen all over US pop culture, though at this point, I have to say it feels rather stale. While it's not an idiom, you could call it a "pop culture reference" or "meme".
Understanding it as a cry for "more excitement" isn't bad, actually, but I wouldn't read too much meaning into it. One of the appeals of SNL was its randomness, and people often quote it quite randomly.
Best Answer
No, this is the name of a specific policy regarding gay servicemen and women in the US military. It is not a general term in the military or elsewhere.
(If you see it anywhere outside of this context, it is almost certainly at least making reference to the military policy, e.g. a satirical reference.)