[84LX89GT]

This should probably be in the windsor forum, but here goes:

This sounds like an EGR problem. The egr system is used during part throttle situations. The EVP sensor measures the movement of the EGR valve and if something doesn't match the tables in the PCM it sends a check engine light that will often flicker/turn on-off.
My '89 GT has that problem because of a .1 volt drop from the connector to the processor, so i have to overlay a wire, but often it is just that the EGR valve is full of carbon and the pintle is stuck. The first thing i would do is take off the EGR valve and clean it out with a de-carbon fluid (lots of things work - carb clean works). Make sure to move the pintle and make sure it's free and nothing is binding.
the EVP sensor is known to go bad as well, so you can unbolt it and with a multimeter measure resistance as you move the rod. You can also use a vacuum pump on the EGR valve and measure volts and backprobe the signal wire and ground to see what the PCM sees. I believe it should read .8 or .9 volts and it can go i believe up to 4.5 volts at the far end of it's range.
If you do replace the EGR valve (usually $70 i think) it's not a bad idea to replace the EVP sensor ($30?) if you have no way to test it and it's easier to replace while the valve is off.