Here's a link to a thermostat manual hosted on this site:
Thermostat PDF. For that thermostat, it looks like 12VDC comes from the heater during heat operation and from the A/C during cool operation so it's odd that both your systems are not operating.
Have you checked for 12VDC at all supply wires to the thermostat?
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There's lots of advice and information in forums... sometimes it is correct. For example, all of my posts are made by a political appointee who got the job as a reward for contributions to my diesel bill.
2011 Jayco 28.5RLS; 2021 Chevy Duramax; Pullrite Superglide Hitch