Too often, and unpredictably, when the thermostat tells our gas furnace to
turn on, all that turns on is the fan that exhausts the moisture from the
combustion. It is not followed up with the flow and ignition of the gas.

If I flip off the master switch that controls power to the furnace, and
flip it back on after a short time, the fan starts up, and the ignition
always occurs.

But if I go to the thermostat and raise the temperature there, by
breathing on it, for example, that shuts the furnace off; but when the
temperature at the thermostat drops back to the ambient temperature, and
the fan starts up again, ignition never occurs.

So it looks like there is a difference in what is shut off by the master
switch and by the thermostat, and that the problem has something to do
with that.

Any suggestions?