Well, I tried to stay out of this one...
But after I saw some success with the not so expensive 1157 red LED lights from Pilot, I went to Walmart to buy some. They didn't have any. So I went to Autozone and got two packages of two, as I have the twin bullet-shaped lights on each side. Naturally they were $20/pair instead of $15/pair
My lights are wired so that all four of them come on for the parking and stop lights, dim for the former, bright for the latter. Both the lights on the same side blink (bright) for the turn signal, alternating bright/dim when the headlights are on and bright/off when the lights are off.
I put in two of the LED lights and all was fine: both sides still did the job they had been doing with the incandescents. So I put the other two in and the fun started.
If I put the first two (good) LED units on one side and the second pair in the other side, the good side blinked properly. The other side, when the turn signal tried to activate it - made the two lights with the BAD LED lights alternate between bright and dim at the same time as the good side indicated a turn properly with bright/off. Picture a funky 4-way flasher with the pair on one side blinking on/off and the pair on the other side side blinking bright/dim.
Rearranging the bulbs into other sockets affected the pattern by switching it from one side to the other, but the GOOD side always worked fine - the BAD side made the other side go bright/dim instead of on/off.
I know, you really do need to see the movie
Conclusion (reinforced by putting good bulbs in all sockets): the BAD LED bulbs had some sort of anomaly, probably a short, causing the odd behavior.
Solution: take the BAD pair back to Autozone and swap for a good pair.
Takeaway: not all LED bulbs are equal, even the same make, model and serial number.
If you don't understand this, I don't blame you!
Tom