f the check engine light is on is it possible that it wont produce a fault code?

If the check engine light is on is it possible that it wont produce a fault code and you have to use the other two testing modes?

My 1991 base 740 has an engine light on and the codes i'm getting arent supposed to set the check engine lamp off according to https://www.volvoclub.org.uk/faq/EngineOBDCodes.html#ReginaFuelInjectionFaultCodes

I have the regina system and im getting an "all clear" 111 in socket 6 and the codes 122 and 233 in socket 2, neither of which are listed as setting off the light. The other two test modes dont produce fault codes, mode 2 responds to tests with codes and simply doesnt respond if the component is faulty, in mode 3 it activates components and you have to check for yourself. If the check engine light is on is it possible that it wont produce a fault code and you have to use the other two testing modes?

It may also be a function of the ecu to set the light if there are more than one code set. So even though those are non check engine light codes. Having two of them may set the light on anyway.

One socket is the fuel computer and one socket is the ignition. So see which computer correcsponds to the socket used and reset that compuer clearing the codes and see if they come back. If they do come back then more diagnosis of the suspected components should be done using the other modes along with verifying connectioins and wiring.

Just to double-verify, is it definitely the "Check Engine" light, and not the "Service" light?

Check Engine (error codes) - erase them and see if they (and the light) come back.

Service (oil change reminder) - pull the rubber plug by the speedo, and push the hidden button behind it.