No, he is seriously wiggling. Not looking back and forth, but head, neck, ribs, hips, all moving in opposite directions, feels like he's trying to trot over debris and trying to feel his steps. If I would try to correct him it would be like, left hand squeeze, right hand squeeze, left leg, right leg -- Yikes! I try to sit still and look forward and relax. I have a feel but not a HOLD, and he is actually going in a line but it's like he's concentrating on each part of his body.
Wiggly means he's got a lot more to work with than he knows what to do with anymore!
Do you both know how to lunge? Get him workin his body without a rider on him. Start with letting him extend himself out. Do spirals on the lunge line and do transition work. This will help him flex his muscles on the circle, therefore rounding and balancing himself (BOTH directions) creating his own natural frame. Once he develops this, continue working him so it becomes a workout. Praise him by transitioning down. Reverse and repeat. Don't get monotonous with 100 circles each way all at once, 5 laps, 5 laps, 3 laps, 4... rotate it, get him really moving different.
Once you take this under the saddle, incorporate the continuous movement forward. Serpentine's, transitions, circles, bend, counter-bend, extend, collect.
Try out some of these exercises throughout the week, and watch for muscles getting more prominent, and your horse becoming more steady with the next step he takes.
Also, depending on your level, feel comfortable adding ground poles, or cavalettis around your arena to focus a bend on, or change of transition. This gets your horse noticing where to place his feet and what rhythm to get into.
Once you both start getting a closer feel for eachother, you'll be back and better than before!