He was talking about an unwanted inevitable consequence involving a rabbinic prohibition, which according to most halakhic decisors is permitted. Tosafot, who disagree with the Arukh regarding an unwanted inevitable consequence, agree that in the case of a rabbinic prohibition it is permitted.

That said, it should be noted that turning on a light is not necessarily only rabbinic.

Tosafot, who disagree with the Arukh*

Terumat HaDeshen too, which the Rabbi cited for his point, is speaking about an unwanted inevitable consequence involving a rabbinic prohibition, and apparently the Rabbi here meant that as well.

Where did you see in the Magen Avraham there that it is talking about an unwanted inevitable consequence? He is speaking about an ordinary inevitable consequence in a rabbinic prohibition.

Indeed, regarding lighting an LED bulb, one must discuss it from the standpoint of building, although according to the overwhelming majority of halakhic decisors it is only a rabbinic prohibition, I am not at all sure of that.

Regarding the legal system in the state—see the article by Rabbi Israel Rozen ("Is There a Prohibition of Gentile Courts in Israel's Courts?", on the Tzomet Institute website) and the sources he cites; the articles by Rabbi Yaakov Ariel and Prof. Yaakov Bazak (Techumin 1–2); and the article by Prof. Eliav Shochetman (Techumin 13).

Best regards, synagogue emissary

I didn't say that the Magen Avraham is talking about an unwanted inevitable consequence. I said that the questioner asked whether he may open a car door that will cause an LED light to turn on, and asked whether it is permitted because this is an unwanted inevitable consequence involving a rabbinic prohibition. About that I said that according to most halakhic decisors it is permitted. Even according to those who disagree with the Magen Avraham.

I'm not a rabbi and I'm a very, very minor Torah scholar, but a comment: the "building" here is weak, because if the construction is permanent then the indicator light loses its value, and therefore there is no nullification of the parts to one another (the Chazon Ish's first rationale?) and also the building from death to life (his second rationale, the weaker one according to his own wording) is temporary.

Ah, I didn't understand that.
But here it is not clear that this is indeed the case. Plainly, this is an inevitable consequence that he does not care about, and on that Rashi and Tosafot disagree (75a), and in practice it is accepted that it is like one he does want (the halakhic decisors do not distinguish). And if it is at night then of course he does want it (because he wants the light). And Tosafot wrote that an unwanted inevitable consequence is like a labor not needed for its own purpose, and there they certainly forbade it even on the rabbinic level.
And also regarding an unwanted inevitable consequence involving a rabbinic prohibition, several halakhic decisors wrote that it is permitted at least in a case of need (Mishnah Berurah 316:5, 321:57).

Moshe,
I did not understand your comments. We are talking about an LED bulb that is based on an electrical circuit, and in that circuit all of this applies.

Indeed, building does apply. But the Chazon Ish explains the "building" in a circuit in two ways (see the Chazon Ish on the page in the passage about a collapsible bed): A. there is nullification of the parts to one another [as I understand it—nullification means viewing them as one for a significant period, as with forceful hammering], and the Talmud does not require strong hammering except to show that the parts are nullified to one another in the mind of the one hammering, and in a circuit too, even with a loose connection there is nullification. B. from death to life, creating something qualitatively new (and this is a weaker rationale according to the Chazon Ish's wording, something along the lines of "it is close to being…" )
A. does not apply to an indicator light for a malfunction, because its whole value is precisely that it is not always lit but only during a malfunction, and therefore there is no nullification, because by definition the intention is temporary.
B. does exist, but only for a short time.

In the Chazon Ish's letter to Rabbi Shlomo Zalman Auerbach, he distinguished this regarding the prohibition of building in an electric bulb, and explained that when turning on an electric bulb, the tendency to turn it off sometimes and not leave it lit all the time is not intrinsic, but only because of "payment calculations"; otherwise the tendency would be to keep the circuit permanently closed (I think he knew this was a strained argument). Even that does not apply in our case.

As I said, in my opinion all of it applies. This is a "hammering in place" for the duration of the circuit's operation, as in any electrical circuit. And likewise regarding the transition from death to life. What I wrote, that I am not sure regarding building—still stands.

When you get the chance, take a look.