OK, this is defintely a new one on me. The check engine light's on in
our non-turbo 1995 850. My trusty OBD-II reader says no codes but
displays all the sensor data, etc., normally and claims to be
communicating with the car both as a Volvo and as generic OBD-II.

Using the diagnostic connector blink code procedure yields 1-1-1 (no
fault detected), confirming what my OBD-II reader says.

Instrument cluster?

JRE

There is a chance to fix it with:
- Take Q-tip and spread few drops of oil over gas cap gasket
- Fill the gas tank.Close it tight.
- Report back in a week or so if CE Light is still on.
Good luck,
Mike