Please clarify what you mean by "control module." Is that within the heater chassis? Or is this something akin to a thermostat, as found in the living space? The "control module" in my forced-air heater is a complex thing. I suppose I could simulate a closed thermostat circuit, at the control module. IT seems your repair man did something like this.
"Thermostat at control module" is unclear to me. I think you mean "thermostat connection terminals at the control module." Well, that tells me that the wiring between the thermostat, and the module, is bad. After all, your actions upon the thermostat, in the living space, were consistently ineffectual. Yet a similar action, with the lengthy wiring between thermostat and control module REMOVED from the process, is effective in consistently activating the heater. You might have also had a bad control module; see below.
THAT'S THE NEW CONTROL MODULE, RIGHT?
That evidences a fault in the OLD control module, too.
So you've got either a flaky interlock switch, or it has shifted in its mount, so that it does not get the right "signal" to change state when the panel is closed. Is this switch a momentary, spring-loaded switch? Is it Hall Effect (magnetically actuated)? So it sounds like you have, or had, three problems. Isolate the interlock switch by lifting its wires from the control module. Then check its continuity, very carefully, under various conditions of panel closure. There should be an unambiguous state change between panel *in place* and panel *removed*. The purpose of the interlock is to prevent operation when the unit is not sealed up. My residential forced-air heater was incapactitated by a panel, slightly ajar. I had to drill and screw, so the panel would not vibrate away from full closure.