It seems to be the indicator stalk being somewhat loose and triggering a switch? But this is the 2nd set of stalks I’ve tried and the same problem occurs, any advise is helpful 
Have you got a “flash to pass” system fitted? In that with the headlights off, if you pull the headlight stalk towards you, do the lights lift? If so, I wonder if however this has been fitted is causing the issue.
I do have flash to pass installed, I’ve googled this problem too and people have reported the same thing happened without it apart from the lights not popping up so I don’t know
Do the front and rear side lights come on too do you know? And is it a UK or JDM car?
It’s only the high beam, the sensitive switch? Is the flash towards the driver I’ve taken an old stalk to pieces to see if I can work out what it could be and feel like it could be one of these guys expanding with the heat
Seems unlucky to get 2 stalks with the same issue though. What’s the detent for the switch like? I’d be looking at sorting the “loose” switch issue next to at least rule it out.
Do they go down when you wiggle the stalk?
If I push it back towards the car yes, it’s like it’s triggering the flash switch slightly, can’t replicate today as it’s not that hot today in comparison 
It’s a while ago but I vaguely remember having a similar problem on my early Eunos and changed the stalk assembly.
I also vaguely remember the way I proved it to be a faulty stalk was by the tried and tested technique of percussion maintenance. Banging the steering column with a fist.
So here’s the thing. You’ve googled it and others have had the same problem so obviously these stalks are prone to failure. I’m assuming the second one you’ve tried is a used part. They are all 30-35 years old. There’s a very good chance that you have had two faulty ones.
I’d try again. Have to be very unlucky to get a third one that failed.
