Do you have a multimeter or vault meter? First thing to check would be to see if the wires running into the indicator itself are live and that the LEDs/bulbs haven't been damaged.
If you're getting a 12volt (or whaetever the voltage is reduced to) pulse with the indicator engaged then your problem is the LEDs/bulbs - which could have been blown form not being installed in the correct polarity. If you're getting a voltage through the wires, check to see it's the same as the functioning side - if there's a significant difference then something else may be amiss.
If you're not getting a voltage signal, then we start tracing it back through the system. The shop manual indicates it's the one fuse - which matches with what I rmemeber. If you have an inline fuse as part of the new indicators you'd know from the fuse holder in the wiring.
The only other thng I'd check s that you're not double grounding it somehow - not sure how'd you'd pull that off, but always a possibility.
Let us know how you go!
Edit: I just re-read your post and bio. I'm guessing you knew/tried all of the above.
I'll have a hunt through the manual for the wiring loom, though I remember having a look at it to see about disabling the auto-indicators (worked it out but never carried thorugh with it - just got used to the bastards). While the indicators are routed through a handful of connectors, there was only one fuse - if it's similar to a three pin connector in hook up too - LHS N/GND RHS. So if you'd damaged it in someway I'd imagine none of it would work correctly.
Unfortunately the manual is 350Mb, otherwise I'd host it for you, but it'll take half a year to upload on my connection - I can't remember where I found it, some dark corner of the internet, I remember struggling to find it though. Having said that, here are the two pages from the 530 odd that contain the turn signal wiring map...
It's the 2012 Vegas/Kingpin/Jackpot manual, but I have a '14 HB and haven't noticed any differences yet.
If the relay's still ticking it sounds like it's still getting voltage. Out of intetest, what happens when you just wire up the old flashers? Might be a really easy, quick check while holding on to them. I'm assuming they were just supposed to connect to the exisiting connections off the loom?
I'd think if you'd fried the input pin on the ECM it would be more than just the inidcator not working... given the circut hooks into a lot more - I could be very wrong, I would just expect to see a larger array of issues, such as neither side indicators/horn/HL/BL etc.
I'm just wondering fi there is a grounding issue, are there new mounts? Is grounding occuring with the mount at all? I'm clutching at straws without looking at it and I'm far from an auto elec - were you able to get any sort of a read with a multi/vault meter?
Sounds like it's narrowed down a little. We know you're groudning properly and the indcators themselves work - it's a start. So did the audible continutiy test sound when for a brief second with the indicator engaged? Beep, Beep, Beep would be a plesent sound right about now I bet.
My next point would be the relay. Reverse poll throgh a relay could theoretucally damage it. Might be worth swapping out with an equivlant (not 100% but check the primary light relay)
Having siad that I've been flipping through the manual some more - the attached may be worth a shot.
Not a problem mate, that's what these forums are for!
I'm just sorry you couldn't get it going, it's really hard sitting on the couch trying to think about it, still not as frustrating as being in your shoes though.
Would love to know if you find out what it is, has me intrigued now. Fingers crossed it's simple and a real no brainer that we just missed.