Proper contact will come with relaxation, straightness and rhythm. In other words, if you set your horse's body up correctly, then he will be inclined to naturally drop his poll. Any other means will cause him to carry a false frame. I'll start first with some things to help with relaxation and if you are interested, I've also added how to work with this issue in dressage.
First thing is your own position, specifically seat and hands. Where you are sitting in the saddle does a lot to influence your leg position and upper body to hands. For example, if you are sitting too far back, then you'll have a harder time not only controlling rhythm, but also keeping a forgiving contact. Here is a website that goes over some different exercises to help find your seat https://www.balancedrider.com/exhorse.htm
. Then, your hand, arm and shoulder position also have a big influence on your horse's relaxation. If you are tense in your arm and shoulder, then you'll be tense in your contact too. Your horse will feel that and will not want to relax. You want your elbow to be relaxed down at your side or very slightly in front. If you have the elbow too far back or too far forward, then your shoulders and arm will become tense. For your hands, they should be closely together, above the wither, and even, with thumbs on top. By the time your looking to have your horse accept contact, they should be able to be steered mostly by seat and leg, so that they can relax into your hand. A good test of this which also happens to help correct uneven hands is putting a crop horizontally under your thumbs. This makes you steer with your seat and leg and makes it so that you cannot use the reins for anything but mabye stopping.
Secondly, is maintaining a good feel of the mouth and allowing give when necessary. Contact is not exactly fixed and we do give forward our hand or rather elbow at certain times to allow the horse to relax down. When I first start horses out in working on contact, I also like to rub the top of the neck (where the trapezius muscle is) with the inside rein to reinforce relaxation. Which puts me at my next point, that the outside rein carries contact, while the inside rein does have more flexibility to give or take when needed, usually in flexion or to reinforce bend.
The other thing you could do without getting too much into dressage training is stretches and massages to help him relax on the ground.
For training, I'd start first with rhythm. You can use rhythm beads, change in your pocket during riding etc for awareness of when he is speeding up and slowing down. Straightness and suppleness are a bit more difficult as they require a feel for the horse's position. For straightness, I find it easiest to work off the rail as it becomes more apparent when they are crooked or drifting to a side. You can do lots of transitions and changes of direction to keep him thinking. A easy exercise is 4 "20 meter" circles: one at A, one at B or E and one at C. As you move from one circle to the other, you straighten the horse. For relaxation, work on suppleness - bending and moving laterally off your inside and outside leg. Also, make sure to keep consistent, but elastic contact with his mouth.
Now for the stargazing, there is a method to deal with this, but it does take time to develop a feeling for it. First, you do not want to punish him by pulling his head down or back, as that WILL cause tension and a negative attitude towards the bit. You do want to maintain contact though, as stargazing is still a way to avoid contact. There are two ways you could go about this: the first is you could keep your hands where they are and wait for him to relax and the second is to raise your hands in line with the bit without pulling and without giving away contact (harder than it sounds). This keeps the bit from acting on the bars of the horse's mouth and instead acts on the corners of the mouth, like it would in a lowered head position. As soon as the horse relaxes (and it is very slight), you start lowering the hands down and forward WITH the horse. This is how you begin to encourage the horse to take the bit down and out. If done correctly, your horse will eventually stretch further down. Timing is essential for the horse to understand and you must keep the horse engaged, but not running at the same time with your leg and seat. Lastly, do this at the walk only until the concept is understood and executed consistently. Then you can slowly start adding the trot. The time you have to do this at walk is often a lot longer than people realize. It can take anywhere from one month onwards not only because the horse is learning it, but also because it takes months to build enough muscle for a horse to carry a proper frame.