Fireplace won't respond to thermostat

I have a Napoleon direct vent fireplace. This season sometimes the fireplace came on in response to thermostat but other times not so I tried two new Honeywell thermostats.
Pilot light stays lit. When I touch white and red thermostat wires together, the fireplace comes on.
When I connect the wires to a thermostat (one old one, Napoleon version that has worked for years and two new ones) and call for flame, nothing happens.
The heat only thermostat has R, W and Y connections. I tried red wire to R and white wire to W. Nothing. I tried red wire to W and white wire to R. Nothing. I tried red wire to R and white wire to Y. The fireplace comes on but does not shut off in response to the thermostat temperature reading.
I tried a more complicated battery operated thermostat that can do both heating and cooling but also can do just heat as for a fireplace. The thermostat responded to my programming instructions. However, I get the same results as the simpler thermostat.
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Judd wrote:

Does your FP have a blower controlled by thermostat? How many wires are there? Checked any loose connections?(that's what happened to one of ours, we have two FPs. W terminal is for heat, G is for fan, Y is for A/C compresser(outdoor unit) Is there a jumper between C and Rh? You mean you have a control board in your FP using a 'stat like that?
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