The idea of having a ner tamid is both an ancient practice, first mandated in the Torah[1] for the Mishkan[2]/Beit HaMikdash, and a more recent practice, as we will see. In the Beit HaMikdash, the “western lamp” of the menora was supposed to always be lit.[3] Now that there is no Beit HaMikdash and our shuls have assumed some of its place in our lives,[4] some say that the ner tamid is among the specific Mikdash-like features that have been adopted.[5]
I have been unable to find a reference to a special “ner tamid” in a shul before the Terumat HaDeshen (15th century Germany). On the other hand, lights in shuls are discussed well before that, and they are an important part of a shul, to which some specific halachot pertain. For example, they cannot have any connection to idol worship or worshippers.[6] This, however, refers to lights in general, and not specifically to a ner tamid.
Some sources refer to the practical need of being able to see and read in the shul, especially at night. Others, including the Rambam[7] and the Rosh,[8] refer to good lighting as one of the ways to show honor (kavod) to the shul. But the contemporary ner tamid is found even in shuls that have extensive lighting and expensive chandeliers; it is usually in the front of the shul, and it stays on even when other lights are off.
Is it indeed required for there to be a light in shul at all times? The Shulchan Aruch[9] rules that it is permissible on Yom Tov to light candles in shul, as the mitzva purpose justifies doing melacha.[10] The Rosh[11] says that it is permitted even to light these candles in the afternoon, so as to have them last into the next day (e.g., into Shabbat or the second day of Yom Tov), because the immediate kavod that the candles bring suffices. Although the Rashba[12] is not convinced that this type of benefit justifies performance of melacha on Yom Tov, he agrees that it is generally proper to have light to enhance the kavod of the shul, apparently beyond that which is practically necessary for reading and the like. The Magen Avraham[13] writes that it is even permitted to light candles on Yom Tov when people are not in shul, as the honor to the shul still applies.
Indeed, it is usually assumed that it is worthwhile to have light in a beit knesset even when it is empty, but that does not necessarily mean that there is an obligation or even a purpose for it to be literally tamid (constantly). The Rav Pe’alim[14] discusses the case of a shul whose members were afraid, for safety reasons, to leave candles lit all night in shul and wanted a non-Jew to extinguish them and relight them the next morning (Shabbat). He states that even when they put out all the lights, they must certainly keep at least one candle lit in a safe place because it is not kavod for the shul for it to be pitch dark. He seems to assume that during the day, when it will anyway not be totally dark, a single candle does not make a difference and is in fact not needed.[15]
Putting things together, nowadays there is a minhag to have a specific ner tamid in shul at all times. Since it is so easy, due to electricity, to just leave it on always, it is unclear whether the minhag mandates that it remain on during the day as well or just that no one bothers to shut it. However, the minhag does not appear to be strongly modeled after the Beit HaMikdash. One of several signs that it is intended for a more practical rather than ritual kavod is the fact that we use electricity rather than olive oil.[16] There are few if any sources that indicate that there is a problem if a relatively short period goes by without a specific ner tamid. Therefore, in your case it does not seem that it was necessary to get candles, especially during the daytime and certainly when emergency lights went on.