You are right that the Check Engine lamp should illuminate at all times when the engine is not running, indicating no reference pulse from the crank sensor. I'd do a quick bulb check first of all, since you obviously can't check codes without a scan tool if that bulb is out.
If memory serves, the dash isn't too difficult to pull apart; the bulb should be either a #194 or #168, some are simply replaceable by removing it from the socket itself, but I've seen Chevy also use bulbs where the base of the glass is bonded to the socket itself. If this is your case, you'd be better off investing in a separate socket and bulb for ease of future replacement.
I've seen in my past vehicles ('85 *-10 Blazer 2.8, '91 *-10 Blazer 4.3) where a loose ground on the driver side of the dash, right above the e-brake release, causes some dash and idiot lights to not work correctly...
I know your priority isn't the SES light itself, but if we can verify the light works but isn't being triggered by the ECM, that gives us a direction to concentrate in... Or at least it helps *me.* LOL
I'd also recommend taking a look at the CalPak, but you already tried an ECM swap (which is not always a perfect diagnosis method, due to Chevy'* occasional wackiness with undocumented one-offs and mid-year changes) so I'm thinking probably not the ECM or CalPak.
This just popped into my head - check the oil pressure switch (the one that turns on the red oil can light). If the ECM doesn't see a buildup of oil pressure in some models, it'll disable the fuel pump. You can crank all day long and there will be no fuel delivery. Also, not sure if this model has a crank sensor, that could be the issue too.
JWFirebird is correct about being two ignition modules, I think GM calls one the "Spark Control Module" in some models. The one in the distributor assembly is relatively inexpensive and simple to replace if you have deft fingers.
I would think it would be better to check the SES bulb and circuit first; otherwise you'd be pretty much throwing money into it until you find the fix.
Good luck, and let us know what you find!