Faulty turn signal switch: The turn signal switch is responsible for sending the signal to the turn signal lights and the instrument cluster. If the switch is faulty, it can cause the rpm gauge and speedometer to bounce when the turn signal is used.
Bad ground connection: A bad ground connection can also cause this issue. The ground connection is responsible for providing a path for the electrical current to flow back to the battery. If the ground connection is bad, it can cause the electrical current to flow through the instrument cluster, which can cause the rpm gauge and speedometer to bounce.
Short circuit: A short circuit can also cause this issue. A short circuit is an unintended connection between two wires, which can cause the electrical current to flow through the wrong path. If there is a short circuit in the wiring to the instrument cluster, it can cause the rpm gauge and speedometer to bounce.
Overloaded fuse: The fuse for the ignition system controls the power supply to the rpm gauge and speedometer. If the fuse is overloaded, it can cause the power supply to be erratic, which can cause the rpm gauge and speedometer to bounce.
Bad alternator: If the alternator is bad, it may not be able to provide enough power to the car's electrical system, which can cause the rpm gauge and speedometer to bounce.
As for the aux red wire from the battery getting hot, this is likely due to a short circuit or overload in the circuit. This could be caused by a faulty component or a wire that has been damaged or pinched. It is important to identify the source of the problem and fix it to prevent any further damage or potential fire hazards.