Hello - I am working on my 1989 Honda Civic and getting frustrated. I swear that previously (when everything was working fine) there was a constant-on light on the ECU with no trouble codes flashing. Now, no light. I have confirmed power to the ECU via the white wire. There is no power to the main relay and no power to the fuel pump. Is it correct that a normally operating ECU has a constant-on light and is the absence of same an indication of a bad ECU?

With Hondas, the CEL should come on for 2 seconds and then go out, when the ignition switch is turned to ON (Position II). This is how the ECM checks out the system. If the CEL stays on, there's a problem with fuses, ECM, main relay, or the ignition switch.

WOW you are fast - thank you! The CEL does not go out when cranking. No light at the ECM at all. Replaced relay, ignition switch and fuel pump. So probably the ECM?

Very likely.

Perform the K-Test on the ECM:

Remove the MAP Sensor connector and turn the ignition switch to ON (Position II). Using a multimeter, check for 5 volts going between the MAP Sensor connector's reference wire (+) and ground. As you look at the connector, this is the socket on the right. Really press the black test lead into a cleaned main ECM ground on the thermostat housing. If the voltage is low, it's probably indicating ECM failure. Most failed ECMs will record a fraction of a volt. To me, the K-Test is simple, elegant, and accurate. Many Hondas parked for several years are now back on the road. "The K-Test creates massive value, by providing a low cost solution where one did not previously exist."--TxGM

As my daughter would say (it's her car) OMG! Thank you!!

Here's how to replace the ECM:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-3.html#post235038