I ride with my hands low, wide and as still as possible to act as side reins. If it is not lack of comfort or a bit they don't like they will usually relax their head and neck towards the end of the first ride.
Maintain outside rein contact while taking and giving on the inside rein.
Maybe you can try and change the bid
I ride a headshaker. They can be a nightmare to ride on their bad days, and it's worse to try and figure out a cause.
How long has he been doing it? Is it worse on some days over others? Is it any particular rein?