There are Atwood
Service Manuals on Chris Bryant's website. Perhaps some troubleshooting.
My understanding is that this is the theory of operation, at last for the Atwood we have, from the early 2000's:
No Thermocouple for Pilot Light. Turning the Oven Temp Knob to "Pilot" opens a tiny orifice and allows the Pilot to be lit and it's a small flame. If that flame blows out, the little bit of LPG still flows. This Oven Control is one of two "valves" in the Oven.
When you order up a Baking Temperature, the Sensor Bulb (not a thermcouple but pretty much a thermometer) causes the Pilot Flame to "Flare" to a much larger pilot flame.
This Flared-Up flame heats the Sensor Bulb on the second valve. When it senses that heat, it opens, and that's the gas that feeds the oven burner.
When the ordered-up baking temperature is reached, the Oven Temp Valve's Bulb senses that and dials the pilot flame back from flared-up to pilot. That isn't hot enough to keep the second valve (Oven Valve, Safety Valve, Gas Valve, various names) open and the valve closes, putting the oven main burner out...
...until the oven cools enough for the Oven Temp Valve to notice that and flare the pilot flame back up to get gas flowing to the main burner again.
I don't want to spend your money, but my guess from you saying the pilot flame WILL flare but the burner doesn't light, is that the problem is in the Gas Valve/Safety Valve/Oven Valve. Not the Temp Control with the knob on it.
OEM parts may no longer be available for an oven that old. They contain mercury and the nanny agencies think mercury is OK for lighting but not for ovens so there are new designs. There IS a company that rebuilds mercury-charged oven controls.