Hi Gary,
Well, I don't really know for sure.
I have never "troubleshot" one of these and have no hands on experience with the 225.
I don't understand how you're testing either.
Continuity means Ohms testing to me.
But, in this case, you're looking for volts.
Do you have 12 volts at the Black/Yellow (Bl/Y) wire at the back of the trim gauge with ignition on? The gauge, being digital, needs that voltage to "turn on" and be ready to work.
Do you have 5 volts at the VCC3 (voltage common control) terminal at the ECM? Light green/Black (Lg/Bl) wire with ignition on?
IF SO....
.....With ignition on, you should be seeing a PORTION of the 5 volt signal from the trim sender to the Yellow/Blue (Y/Bu ) wire at the trim gauge terminal.
The portion should likely be between 0.5.v to 4.5v depending on the trim sensor position and should change as the sensor angle changes. I can't give you specific voltages but that should be fairly close.
When you probe the Y/Bu wire at the gauge, put your red test lead on the wire terminal and the black lead on a reliable ground. Don't use the the Black (Bl) wire at the back of the gauge for connecting to ground because you don't know if it is reliable yet.
Make SURE the ground you choose for testing is a good one by testing for 12 volt power at another location using that ground. Many times a poor ground will invalidate your testing.
if you don't have 5 volts from ECM with Key On Engine Off (KOEO), try starting the engine and check again Key On Engine Running (KOER). Make certain that you're using a good ground!
If no 5 volts at ECM in either condition, I would have to say the ECM may be faulty. But, again, I have no experience with this and very limited service info.
If you find that you have the portion of the 5 volts signal at the trim gauge Y/Bu terminal that changes as the sender angle moves AND you have 12 volts at the Bl/Y wire then either the gauge is bad or the ground for the gauge is not a good one.
You could use a jumper wire to provide a reliable ground for the gauge to see if that's the problem.
I hope this is understandable to you....
...if not, my apologies.
But, I'm sorta wingin' it using my phone and a free pdf service manual wire diagram which is fairly difficult to read.
But always happy to discuss the issue and answer questions.
Let me know what.you find.
Good luck.