Say what you will about modern cars being too complicated for their own good -- at least they're fairly predictable. In the decades between about 1975 and 1996, computer diagnostic systems were more of a gimmicky service tangent to fuel injection that anything coherently useful. As such, it's only natural to wonder exactly what these older systems cover, and how well.
The General Motors computer systems of this era -- known collectively with all others as OBD-I systems -- did indeed monitor and test EGR functionality. It has several EGR codes that will trip a check engine light in the event of component failure. Codes 32, 53 and 54 indicate a malfunction in the EGR electrical circuit itself, and the latter two indicate a circuit failure because of low voltage. Codes 75, 76 and 77 indicate that there's a failure in the EGR solenoid itself.
Checking the OBD-I codes in a GM car is the standard "blinky light ALDL" procedure. Find the diagnostic port connector, and locate the two terminals -- known as terminals "A" and "B" -- in the top row, far right of the terminals. Connect the two terminals with a paper clip bent into a "U" shape and count the number of times the check engine light flashes. Long flashes for the "10s" place, short flashes for the "ones" place, then a pause between codes. So: seven long flashes, six short flashes and a pause give you a code 76.