The symptoms you're describing, where the lights flicker and the headlights lose intensity when you start the engine, can be indicative of several potential issues. While you've already checked the battery voltage and alternator voltage, there could be some other factors at play. Here are a few possibilities to consider:
Weak Battery
Even though the resting voltage of your battery is 12.35V, it may still be weak or have a bad cell. When you start the engine, it places a significant load on the battery. If the battery is not able to provide enough power during this process, it can lead to flickering lights.
Battery Terminal Connections
Ensure that the battery terminals and connections are clean and tight. Loose or corroded terminals can result in intermittent electrical issues.
Faulty Alternator
While your alternator voltage seems reasonable, it's still possible that the alternator is not consistently providing the necessary power. Sometimes, alternators can have intermittent issues, and this might not always be reflected in the voltage readings.
Voltage Regulator
The voltage regulator is responsible for regulating the voltage output of the alternator. If it's malfunctioning, it could cause fluctuations in voltage, leading to the symptoms you're experiencing.
Grounding Issues
You mentioned that the grounding seems good, but it's worth double-checking all ground connections, especially if the issue is more pronounced in colder weather. Cold temperatures can sometimes affect electrical connections.
Electrical Shorts or Faulty Wiring
Inspect the wiring and connections in your vehicle's electrical system for any signs of damage or corrosion. Electrical shorts or damaged wiring can lead to voltage fluctuations.