Hello, those are symptoms of a defect in the printed circuit card... that is here the thermostat wires connect inside the furnace and everything else plugs in.
Stress test the printed circuit card.
Use a hair drier to slowly and gently warm the card to 120F(warm to the touch but not hot and not over140F)... if you get any change in behavior that means the card is bad...
A micro crack has opened in the printed circuit at a solder joint, or inside its CPU in that case .... or a short circuit has developed as the card expanded when you heated it.
Constant expansion and contraction as these electronics heat and during their duty cycles over the years is what wears these cards out.
It is also a good idea to replug all of the connections in the unit,that burnishes any oxidized terminal connections and will sometimes solve the problem, especially at the printed circuit card and in any sensor molex connectors. Do that with the power off to the unit of course.
These cards are also damaged by Electrical Spikes caused bypower failures and lightning. These high voltage spikes can literally explode the fine 'wire' connections inside the chip.There is also a shunt type device, often printed on to the card that allows a high voltage spike to arc across to ground harmlessly, some of these can wear out after a few times and allow the high voltage spike into the rest of the card and the CPU micro-circuits. The high end printed circuit cards use a large capacitor like device, or several in parallel, to capture and release such surges, these do not wear out.
Let me know what you can discover, we can go from there as needed.