First, I'm gonna assume this is about a Gen2 Duke...
and I may be wrong because you haven't indicated...
so this may only be an experiment in the random psychology or surreal cosmic nature of diagnostics...
Ok, look at it like this:
It is only vaguely productive for you to evaluate injector circuit control the way that you currently are.
I think perhaps that is also [way too many syllables] only to be paraphrasing the idea
that won't work.
By the way, super scores for having a DVOM,
and for being willing to actually jump in and use it...
But what you should be doing with it instead is
*evaluating the voltage level on the Brown/White wire, via back-probing the socket
*with the injector plugged in
*with the key on
*with the black DVOM lead attached to a legitimate frame and harness ground.
If you do that and you have an actual 12V, then you
do not have a power supply issue.
But if you only have around 9 or 10 or even less volts, start back tracking through the diagrams I uploaded...
until you find out where the full 12v exists.
IOW... is it just a poor connection, or a fuse that only
looks like it's good, or is it a bad relay??
Stuff like that.
Ok, so now it gets just a little trickier.
If you have 12v at the injector, all you really want to know now is
a) does that 12V also exist on the downstream [Blue/White] side of the injector, with injector plugged in and key on...and
b) can the ECU pulse the Blue/White Injector line.
If you have a test light, you can hook one end to ground, and the probe end into the Blue/White cavity,
with the injector plugged in of course, then crank the engine.
If the ECU is pulsing the injector, the test light will toggle on and off.
But there is no reason for the injector Blue/White wire to be in a ground state with Key On Engine Off...
so if you didn't prove 12V on the Blue/White with the key on, and injector plugged in, is the injector electrically open?
Test it's internal resistance, unplugged, with your DVOM. Is injector resistance between 12.8 and 16.8 ohms (corrected)?
If all that works/proves itself good,
go back to the first thing you should have done.
Grab a stethoscope with a long thin probe, and have a friend crank the engine while you listen carefully to the body of the injector. Listen for the cyclic 'clicking' sounds that prove the injector isn't simply
stuck.
Sorry bout the long litany, this is sooooo much quicker and automatic when I'm just
doing it.
but...
I hope it helps.
Post back, of course, so we know what happened.