Here is a possible scenario that could cause this:
Have you possibly rewired the headlight?
Either at the lamp connector socket itself or at intermediate connector going to the lamp?
The two lamp filaments of course have a common 'ground' - there is no way to separate that.
When wired up correctly, with the High, Low and Ground to the appropriate terminals of the bulb, you get the scenario shown on the left of the diagram below.
Current will only flow through the Low Beam or the High Beam, whichever input is active.
IF however, the Hi and Ground wires to the lamp connector were swapped, you would get the scenario on the right side of the diagram.
What would happen if this were the case is that when the Low Beam is selected, the voltage would be divided across the two filaments and current would flow through BOTH of them
(you would get lower voltage across the High Beam Filament because it has lower resistance vs the Low Beam Filament)
That would ALSO give you approximately 5V OUT on the High Beam wire, enough to make the High Beam Indicator glow
Of course both filaments would actually be on in this scenario, but both with less intensity being at ~ 1/2 voltage on each.
So it might not look that odd.
Then when you go to the High beam, you would get the full 12V across the Hi Beam Filament and to the indicator Lamp
No current would flow through the Low Beam filament in this switch position, only the high beam (& indicator)
I obviously don't know for sure whether this is your problem, however if mis-wired like this, it would certainly give you that exact symptom
Worth checking!
(Simply unplugging the headlight connector will tell you if this is possibly the problem - if the 5V goes away and the LED goes off, it is because of this scenario)
(I've drawn it two different way diagrammatically but they are both the same electrically - not sure which one might be easier for you to follow - in either illustration simply stated the High Beam wire is connected to the Ground Terminal of the Lamp and vice versa)
Hi Beam_Issue.png (42.04 kB . 768x576 - viewed 398 times) Hi Beam_Issue_2.png (39.41 kB . 768x576 - viewed 386 times) H4_Socket.png (413.55 kB . 640x555 - viewed 361 times)