If horn and heater are on the same FUSE check here for a corroded fuse first, heater earth will be seperate to the horn.
When you say stopped working you mean the motor, I assume (?).
The switch works by sending the currect to each position of the RESISTOR pack on the heater blower motor, your readings are very low, I would clean up all the battery connections as well just so they can be ruled out.
Is it just one particular speed it does not work at, if so it will be a broken resistor pack wire, most blikely or a break in the wire between it and the switch.
What is the battery voltage with engine off and engine running ?
You sound like you know what is what lecky wise so will not be a hard fix.
DC motors(heater blower) are exceptionally voltage sensitive, so make sure you have decent volts to start with.
tabetha