How about the full model number so that I know what ignition system you have. They used more than one design on that series oven.
Being you said a pilot, That means you probably have a Fenwal gas control with a spark lit pilot. If you are not a tech with the knowledge of how to use a DVOM, You would be best served by hiring one.
Why I say the gas control system? Well you say that it lights and then goes out. Most fenwals for blodgett have a 50 second delay looking for the flame current before locking out the pilot. If they see the current, they open the main valve. Simple as that.
How is the current generated? The control has 24 VAC that is sent out to the flame rod. this is insulated and does not touch anything but a flame when lit. The flame rectifies the electricity and a small amount goes to ground of the pilot burner on this machine. Sometimes main burners of others. The pilot is grounded to the controller. and the controller determines that there is a DC current to make a decision.
Guessing at replacement is costly. What one has to test is for the flame sensing current to the controller. This can be the pilot, flame rod, wiring, or burner grounding. Or a loss of power or signal to the gas controller. And on rare occasions the controller itself. We are talking mere 1 micro amps of DC current here, so knowledge and use of your meter is very important. And not all DVOM’s have a micro scale. Your problem may be as simple as a dirty terminal or flame rod. Corroded ground wire connection, Or even a bad insulator or not in the flame properly.. Little things that a tech spots right away.