Furnace not blowing air

4 flashes is ahigh limt switch open or a 24 volt fuse open . Which could be afaulty blower or a blocked air filter .

https://fireplacehubs.com/york-furnace-red-light-blinking-7-times/

https://upgradedhome.com/york-furnace-red-light-is-blinking/

The switch is not the problem ,it is doing it job.
Locate your vent and put a bend over it because what is happening is on windy days wind will get into vent blowing that combustion air back to furnace causing pressure switch to tripped.

A steady heartbeat on the circuit board USUALLY means normal operating condition.

It sound like the limit switch is shutting off and not coming back in to play .

try to replace your thermostat and conduct observation with your furnace if happen again after replacement of thermostat furnace also damage.

Sounds like there might be a bad ground or wire connector.If you are not good at chasing wiring I would take it to some one who is . Good luck

Problem: Your furnace will not ignite the gas to produce heat for your home. When a furnace has a bad ignitor what I see most of the time is the following sequence of operation:

1. Thermostat calls for heat. 2. Draft inducer motor starts. 3. Pressure switch attached by a small plastic or rubber tube senses the negative pressure produced by the draft inducer and closes. 4. Draft inducer runs for 30 seconds to a minute before you hear a gas hissing sound. The ignitor did not glow, the flame sensor (a small metal probe about 1/8" in diameter, with a white porcelain base) does not sense the flame, so after 8 to 10 seconds the hissing sounds stops with no ignition of gas to heat your home. Your furnace shuts down and goes into a lock out condition until you turn your power switch back off and on again. Then the sequence starts all over again with no ignition of the gas. Solution:You probably need to purchase and install a new ignitor. I would suggest that you inspect your ignitor closely for cracks. Make sure you do not touch the ignitor with your bare hands. If you do not visually see a crack, then you could have a furnace control board problem or a limit, rollout switch problem. The furnace's control board might not be supplying the voltage to the ignitor. If your furnace lights and the gas stays on for 8 to 10 seconds, then shuts right back off, then you need to clean your flame sensor with light sand paper or steel wool. You might need a new flame sensor, but most of the time they can be cleaned an will work well after cleaning.

ok this is going to sound funny but it seems as though the polarity is reversed going into your furnance. to correct this proiblem you first need to unplug the unit and where the cord goes into the furnance at that connection disconnect the two wires. Once theses are disconnected switch the wires .All you are doing is reversing the way the electricity flows into the circut board. I would wager that is the problem

Defective combustion air switch. The 3 blinks are an error code. You didn't say, but I'm guessing you have a Coleman Evcon. They had alot of defective Combustion air switches. Your specialists were not that.