None of the ways I have tried seem to be easy, so I would be interested to hear what others do as well.
A coping saw works, but takes a while. It's not very precise in my experience either (that could be me though).
Something else I do (and this works better for me) is to take a chisel and mark off a line where I want to knock things out. I then take a hammer and chisel out what I don't want. Once finished I then have to take a rough file, or rasp, and clean up the chiseled out part. It rarely looks pretty once finished (thankfully that part is inside the box and not seen), and isn't very easy either... but effective.
I have tried notching out a small section with a saw or chisel and then using my electric scroll saw, or even bandsaw, but with blade wander it is hard to get straight, consistent cuts (or without breaking a blade on the scroll saw).
Here's a video of Glenn Watt showing how to do it using a coping saw... https://www.youtube.com/watch?v=2W6A38lMgJ0
Try this, Brian:
Drill sideways through the neck near the bottom corners of the notch (technically, it's a dado.) Thread your coping saw, jigsaw, or scrollsaw blade through one hole, and cut more or less straight across to the other. Use a hand saw to cut down the edges.
This will leave you with roughly half the thickness of your drill bit along the bottom. Clean it up, don't clean it up, who cares?
If you do want to clean it up, a sharp chisel is a good choice. If you don't have a sharp chisel, a rasp of some sort will do it for you.
You could try not notching it out. Attached in progress pic of a now completed CBG.
The neck is built up rather than carved. Pic should be pretty self explanatory.
I really like the way that looks, Matt.
I use a dado head on my table saw
I use an oscillating power tool I picked up for another job at Harbor Freight. I use a plunge saw blade.
For the necks I build (1 1/2" inch wide) it works great! Just be patient and make sure the neck is clamped to the table.
I am using maple. The saw cuts fine but does get a little hot.
When I get done with the rough cut, I follow up with a rasp and sandpaper to smooth things out.
The difference is the Dremmel spins and this goes back and forth.
I just picked up some blades when I was at the store. I think they are 1 3/8" for wood.
So what I do is cut in from the side. The blade will easily handle 3/4" so that gets you half way through a 1 1/2" maple neck.
The cut can leave burn marks in the wood. These needs to be sanded out if you are notching the head stock.
I think Dremmel has their own version of this but Harbor Freight is dirt cheep. Fortunately, I have one not too far from my house.
Hope this helps.