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1990 Caravan, 2.5 turbo, automatic. If my 02 sensor was bad, wouldn't I get a code flashing when I check for one?

Nope, o2 diagnosis is not a priority for that old of a system. Even OBD2 systems can have faulty o2 sensors and not flag a code and they have many potential codes for o2 sensor issues. Since they are cheap and fairly easy to replace that would be my recomendation. Next would be to check cam timing.