"...see if I understand-the ECU grounds the injectors to fire them..."

Yes.

"...and the signal to do so travels through the RSR..."

Not quite.

Power is supplied to the injectors via a power relay, which is labelled the "radio suppression relay." This relay acts like a simple switch -- flipped on when the FI system is powered, flipped off when it's not powered. This means that injector power is supplied by (and contolled by) wires that do NOT run near the radio. Hence, the use of this remote (underhood) relay suppresses radio interference that radiates from those power wires. (Switching the injectors on 'n off cretaes tons of high frequency radio noise, called "rfi.")

"IF the RSR is good it should click when the key is turned to the on position-correct?"

Not quite.

While it must click, it must ALSO provide the power through when it clicks. Very often, the solder connections that first fail are the heaviest connections -- the same ones that carry the heavy current.

"...does this indicate a bad ECU?"

It might. But these FI control units are remarkably robust (except for the flakey units used in the '89 240s).

"...test the ECU in order to determine whether or not it is in fact bad?"

Sub it in a like-minded car (same "brain") and see if it works.

Far easier to test at the injector for the presence of 12 volts when the relay pulls in. You should find the "noid" lights that plug into the harness in place of the injector.

"...tried to test the resistance/voltage/etc...on the injector harnesses with a digital voltmeter, could I have damaged the ECU by doing this?"

It's not impossible, but it's not likely. The output circuit is low impedance (because of the high frequencies involved).

=================================

Unplug an injector and put your DVM probes into the harness connetors. Look for 12 volts. Crank the engine and see if the indicated voltage flickers or drops in any way.

Also try measuring using the AC range. A steady DC voltage should indicate 0 volts (using the AC function of your meter) but you'll see some indicated voltage if the DC starts to pulse.
--
Don Foster (near Cape Cod, MA)