Here are the most important driving rules to follow when driving in Cozumel, Mexico:

1. Drive on the right side of the road: In Cozumel, as in the rest of Mexico, vehicles drive on the right-hand side of the road. Stay in the right lane unless overtaking and be attentive to black arrows on white background - they point directions for one way roads. 

2. Observe speed limits: the speed limits are between 40 (in town) - 80 (ouside of town) km/h (25-50 mph).

3. Wear seatbelts: Seatbelt use is mandatory for both the driver and all passengers in the vehicle. Ensure that everyone in your vehicle is properly buckled up.

4. Follow traffic signals and signs: Obey all traffic signals, including traffic lights, stop signs, yield signs, and other road signs.

5. Use indicators and signal properly: Always use your turn signals to indicate your intentions when changing lanes, making turns, or merging. 

6. Give way to pedestrians: Pedestrians have the right of way at crosswalks and intersections. Always yield to pedestrians and exercise caution when approaching pedestrian areas.

7. Avoid distracted driving: Using a mobile phone while driving is prohibited in Cozumel. Keep your focus on the road and avoid any activities that may distract you, such as texting, making phone calls, or eating.

8. Do not drink and drive: It is illegal to drive under the influence of alcohol or drugs in Cozumel. The legal blood alcohol concentration (BAC) limit is 0.08%. 

9. Respect speed bumps: Cozumel has numerous speed bumps, also known as "topes," particularly near towns and residential areas. Slow down when approaching topes to avoid damage to your vehicle and ensure a smooth ride.

10. Be cautious of wildlife: In some areas of Cozumel, wildlife, such as iguanas and other small animals, may cross the road. Drive cautiously and be prepared to stop or slow down if you encounter any animals on the road.

11. Watch for bikers:  Traffic in Cozumel is overall very tranquil, but those driving scooters and bikes tend to speed, ending up in your plind spot.

12. Carry your license and a copy of your visa/permission to enter the country at all times: Unfortunatelly a rented car is more likely to be stopped at a police check point if there's such. 

13. Don't use the bike lanes for overtaking even "for a quick second". They are for bicycles and scooters only – not for for passing cars, bikes and pedestrians. 

14. Watch for one way roads: Unless you are on one of the main avenues, it is very likely that you are on a one way road. Ba careful! Some of these streets have "STOP" sign (also known as ALTO) on every intersection. 

By following these important driving rules, you'll ensure a safe and enjoyable experience while exploring the beautiful island of Cozumel.