Answer: The Mishna (Berachos 51b) teaches that one doesn’t recite the beracha, borei meoiray haeish, unless one benefits from the light, though there is a machlokes in the Gemara (ibid. 53b) as to whether one actually needs to benefit from the light or not. Thus, Rambam (Shabbos 29:25) and the Shulchan Aruch (OC 298:4) write that one should ensure that the flame is close enough so that one would be able to distinguish between various types of currency.
While R’ Moshe Sternbuch (Moadim Uzemanim 6:90) writes that he switches the lights off during havdala, elsewhere (Teshuvos Vehanhagos 5:86) he writes that one would still say amen upon hearing the beracha while the lights were on, as if necessary, one can rely on the electric lights themselves (See Rivevos Ephraim 2:115:32).
Similarly, R’ Menashe Klein (Mishne Halachos 15:92) writes that there are some poskim who even allow using an electric light for havdala. He compares our scenario to many people lighting Shabbos candles next to each other. While everyone’s candles only add a little bit of extra light, one still performs the mitzva of lighting. Likewise, there is no need to switch off one’s electric lights when performing bedikas chametz with a candle. Based on all of this, he writes that there is no need to switch the lights off.
R’ Dovid Ortenberg (Tehilla Ledovid 298:4) writes that the language of the Shulchan Aruch (and others) implies that one doesn’t actually need to benefit from the light. One simply needs to be close enough that they could distinguish coins from each other. The Piskei Teshuvos (298:5) writes that this is why we typically recite this beracha even where there is otherwise ample light.
In conclusion, there is no need to switch the lights off during havdala before saying the beracha, meoiray haeish.