On a traditional bike, aka restored. The turn signal wire seem to end with the indicator light. Since you have done all the wiring, it will be easy to figure out. The issue with the restored going to LED is that the ground element, is used by the indicator light. If you go to the superbrightLED website, they have a metric diode kit, for the restored normal issues systems. So here is my thought, if your still using the traditional switch (short term memory, I think you said you have a toggle on/off/on. Some where there is a ground spot.
solution: the Metric kit from superbright is isolating the ground to specifically the left or right lights. it does that by splicing into the system, and adding a ground, then (diode) does not allow for cross stream contamination, (ghostbusters, don't cross the streams) which is what your currently doing. you have one ground, and you need to figer out how to uncross the streams.
For me, when I discovered this, (previous to get the metric kit) I was able to check every line, and then the eureka moment was when I pulled the indicator out, and if I remember right I had flashing lights working, Or not working because the were not ground. I am not going to add pics of what I did, cause you don't have the brown wire. I remember my thought at that time, is !That is why Yamaha went to 2 arrow indicator lights in 1982 and newer. TMI, fine back to the back row pews for me. (BBS360 your right on, as usually, thanks for being here!)
Video wont post if its too big, post it to Youtube, then in advance mode, you add the video to the post. You tube gives you some privacy if you only want to share it if we click the link, or (activated by post) then you don't have to have it searchable with all the millions of other short vids.