When ever you are troubleshooting the thermostat wiring on a Nest thermostat it is always nice to have a basic electrical meter like this one. The Nest thermostat has press connectors for the thermostat wiring connections. The press connectors are designed for only one wire each. If your existing thermostat had a jumper between RC and RH do not install a jumper between the RC and RH terminals on your Nest thermostat. The Nest thermostat automatically internally connects the RC and RH terminals if needed. Below are typical Nest thermostat wiring diagrams for air conditioning and heat pump HVAC systems. The wiring colors shown below are typical. Your thermostat wiring colors may not be the same color. You can use this thermostat wire.
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Typical Nest thermostat wiring diagram for a 1 cool 1 heat HVAC unit
Typical Nest thermostat wiring diagram for a heat pump unit