First for the easy part of your question - yes, a command is a command whether its verbal or signaled - one of my own personal bugaboos in the ring as I tend to use a lot of "body English" and in competition that will get you dinged.
The rest is a great question, but there's not a simple answer
When teaching a command, the way I have been taught, is you don't say the command until the dog is doing what you want reliably. For example if I'm teaching a "sit", I would either lure or free shape it until the dog is reliably offering a sit for a click - at which point I would add in the verbal or hand signal or both. (Often when you lure a behavior, the luring movement is closely related to the hand signal, and you just tone it down.)
Teaching commands this way eliminates inadvertently teaching the dog that the command is "sit, SIT" instead of one "sit". (Or if you train with escape/avoidance that the command is "sit, no, SIT".)
Now, unless you're a genius trainer with an equally genius dog, at some point you're going to give your dog a command and they're either going to stare off in to space or look at you like you've grown three heads and started speaking in tongues. Or, if you have an overachiever-type you may have one of those moments where you say "sit" and the dog goes in to a chain of 14 different behaviors before finally plopping down and looking at you like you are the biggest bore on planet earth.
What you do at this point depends on your ability to figure out why the dog is missing the command. A lot of dogs miss a command in real life settings because of lack of focus. Well, more accurately, not "lack" of focus, just that their focus is on anything other than the owner - kind of like trying to talk to a man who's watching football. In this case, I would regain focus (for me that's saying the dog's name, or "ready") then repeat the command. Some dogs you have to move to another location entirely. But the idea is that you deal with the lack of attention on you, more so than the missed command. And note to self - don't ask for a command when your dog is actively ignoring you as you have just set the both of you up for failure.
Its all about attention/focus on the handler, and if you don't have that, stop what your doing and regain it. I see so many people focus on the behavior itself instead of focusing on the fact that the dog is way more interested in the other dogs in the room. Regain and learn to maintain the dog's attention in the face of distractions, and the behaviors will take care of themselves.
If I have a dog who misses a down because he's not focused on me, I'm not going to work on proofing downs as much as I'm going to work on maintaining focus during whatever distracted him.
Some dogs are the kind that get in to what I call "system overload", and like an old computer with too many windows open at the same time, and you check your task bar and it says "program not responding". That's my dane girl. With her you have to do a forced quit and re-start
With a dog like this I like to make them move. Walk off, then return to where you were working and try again. Some dogs just need three steps, others need a walk around the block.
So a really long answer to say that yes, you repeat the command
But the important part is do you know why the dog missed the cue, and what do you do between the failed command and repeating it to remedy why it was missed.
Oh, and wanted to add - sometimes you get something you didn't ask for. Like you ask for a sit and you get a down. This is where NRM work really well. I would NOT correct this kind of thing as the behavior offered isn't a "wrong" behavior, (I might want a down later on) its just not the right answer at this moment. You don't reward, ask again, and reward compliance. I'd always rather the dog offer something than nothing at all.
