Ok, I have a 1991 Z28 350TPI...newly rebuilt in Feb.

It runs fine but very rich. I replaced the 02 sensor but it didnt help.
The tailpipes are black inside and on my finger its wet and wreaks of fuel.
I'm concerned not only of gas consumption but that it may soon clog up my cats.

 

Check the codes in the ECM first, let us know.

Could be many things, but let's see what the ECM thinks is going on first

 

Would I have to check the codes even if the SES light never comes on?

 

I'm guessing, from the nature of the questions you're asking, that you just bought this car.

Try a new light bulb before attempting to pull the codes. You may find that it never goes out, and perhaps even that the PO "fixed" it by removing the bulb.

 

I've seen the SES light come on before, just after I got it out of the shop in Feb. It came on and off for a few days but stopped after I installed new air filters and drove it a while.
I'm going to go purchase a new GM 02 sensor. I installed a Bosch which later was told was not a good idea.