Coordination is a skill, so it improves through varied, deliberate practice rather than through general fitness work. Practise the specific movement slowly with full attention, then gradually add speed, complexity, and unpredictability.
There is no single general coordination trait that transfers everywhere. An excellent gymnast is not automatically a coordinated boxer. Improvement comes from practising the actual patterns you want to perform, which means the first question is always what you are trying to coordinate.
Varied practice, where you rotate between related tasks rather than repeating one identically, produces slower progress within a session but better retention and transfer. Practice that feels a little harder and less immediately successful is usually building more durable skill than practice that feels smooth.
Ladder and line drills, A-skips and B-skips, bear plank shoulder taps, and contralateral patterns such as bird dogs all develop limb coordination and rhythm. Treat these as a supplement; the specific skill practice remains the main event.
Coordination improves fastest when you are fresh and concentrating. Placing skill work at the end of an exhausting session trains fatigue tolerance instead. Short, frequent, attentive sessions beat long, tired ones.
Early learning always looks worse than the compensations you already have. That is a normal stage rather than evidence the approach is wrong. The neural background is in The Nervous System and Athletic Performance.