Ok, I'll try to explain in words, but it's easier to show.... So here goes...
I know you said you want to not use a bit, but it works best to teach this at first with a bit so they have an idea of how to respond, but you can start with a halter or move to a halter shortly after.
Stand still on his back with your body relaxed so that he won't back up. Take hold of both of the reins. Try to hold one a bit shorter than the other so that it's harder for him to lean on the bit. The best place to put your hands after you have hold is up against your thighs. Because it is more to the side and straight back instead of back and upward it is easier for him to understand what you want. Also, because you have your hands up against something stationary it's easier to tell when he softens.
At first he will probably feel tight and maybe even like he's pulling on the bit. Yes, this does happen even if they have vertical flexion, but we're working on softness and lightness and then head posture will follow. You need to hold your hands stationary until you feel him soften up when he's NOT moving, if he's backing up just wait for him to stop. When I say "soften up" I mean that he will bend his neck better and loosen his jaw to you. That's him pretty much saying ok I give. The instant you feel him soften give him release give him a giant release from pressure. The best way is to kinda throw the reins onto his neck, but if he likes to go, this isn't always the best idea, and I just move my hands really far forward quiker.
At first it is a really long waiting game and just hang in there! Even if you feel like you aren't getting anywhere, he'll catch on quick. Just don't give up, and if he's taking FOREVER to soften the first few times tighten that shorter rein a tad bit. Oh, another thing! Start with a little bit of tension at first when he's still getting the idea, but later you can add more. It's really great being able to see them learn how to soften up, and they are sooo much more fun to ride!
After he has a really good idea of how to soften using the exercise you can have him soften for longer times, maybe 3 seconds then release, then 5, and so on. Also you can do this at different gaits. Just start from the begining of the exercise for each gait, but when you are moving it's a really good idea to have your hands on your thighs because it's hard to tell when he softens otherwise.
Soon he'l know that whenever you pick up the reins he should soften. And for the western pleasure one, I've found that you can just touch them w/ your legs at the same time you pic up on the reins to get them back on the vertical with out changing gaits.
Hopefully that helps, and feel free to ask any questions!!