My Arab sounds a lot like yours with his wiggly neck and tendency to balk and gawk. Keeping him focused, forward and with contact is key. In lessons we have been doing some exercises that really help him stay soft, supple and working.
First, if you feel he is about to spook or gawk, ask for bend away from the source while leg yielding toward it. This means a really strong inside leg, outside rein with lots of forward. If necessary, use a crop to reenforce the forward movement. Basically, the second you feel your horse say, "I'm scared", you respond, "Lets get to work".
As for exercises, we have been doing lots of 10, 15 and 20 m circles with many changes in direction, gait and speed. I find this really helps my guy to focus on me snd he becomes wonderfully soft, supple snd responsive with these. Here are 3 patterns I have found really helpful to get my horse to respond better with suppleness and forward.
1. 10 m circles - lots of direction changes for suppleness.
Proceed down the center line trotting from A and do a 10 m circle right through F back to A.
Continue down A and change the bend to prepare another 10 m circle left through K.
Continue down A, change the bend and circle right 10 m at B then left, 10 m at E.
Continue to C and circle right 10 m at M and then left 10 m at H.
Track left in extended trot H to K ( push for forward here).
Turn up at A and repeat the pattern.
2. 20m circles at A and C with extension and forward down the long sides.
You can out in some canter / trot or walk / trot transitions on the circle as well.
3. 10 m circles up the centreline alternating directions.
Trot through C on the right rein and circle right 10 m (to the quarter line) then trot left 10 m to X. At X, circle right 10 m to quarter line, then circle left 10 m through A. Be sure to straighten and deliberately change the bend each time between direction changes. It is fast, so your cues have to be very timely and precise.
You can revise this by leg yielding out to 15m circles on either side of X.
Rather than using poles, or pilons to intentionally go over and around, I would place a few items in the riding space and simply have your horse work with the scary objects present. Focus on having your horse stay responsive and working despite the objects. There are always poles, jumps and pilons out of the way, but in the arena where work. My guy has learned to deal with these distractions and listen to my cues very well. He has translated this to the trail also. Rather than balk at new objects (like he used to) he looks for my cue to put him back in focus.