What was the size of the Ner Tamid in the Temple? Was it large enough to be a useful source of light? Or was it small and symbolic?
The Ner Tamid is actually a reminder of the Menorah that stood in the Temple. There was no Ner Tamid as we have it in shul in the temple. I think that you mean the menorah which was lit every day (tamid as continually not always burning) and burned as long as the oil each day lasted. One of the miracles of the first temple was that the westernmost lamp lasted from the initial lighting until it was put out to relight the menorah for the next day.
An Eternal Light (Ner Tamid) hangs above the ark in every synagogue. It is often associated with the menorah, the seven-branched lamp stand which stood in front of the Temple in Jerusalem. It is also associated with the continuously-burning incense altar which stood in front of the ark (see First Kings, chapter 6). Our sages interpreted the Ner Tamid as a symbol of God's eternal and imminent Presence in our communities and in our lives.
Vayikra 24:4 The Ner Tamid referred to is the menorah. The western most lamp of the menorah stayed lit until the rest of the menorah had been lit.
עַל הַמְּנֹרָה הַטְּהֹרָה יַעֲרֹךְ אֶת הַנֵּרוֹת לִפְנֵי יְהֹוָה תָּמִיד:
Upon the pure menorah, he shall set up the lamps, before the Lord, continually.
pure menorah: [The menorah] which was [made of] pure gold. Another explanation [for “Upon the pure menorah”] is: [He shall set up the lamps] upon the purity (טָהֳרָהּ) of the menorah, because [before kindling] he would first clean it up (מְטַהֵר) and clear it of ashes [from the previous night’s burning]. — [See Torath Kohanim 24:218]
According to Temple Institute
The Menorah was eighteen handbreadths high (about 1.80 meters) - the height of an average person - from its base until the top.
The menorah weighs one-half ton. It contains forty five kilograms of twenty four karat gold.
I have seen replicas that seem to imply that the width was also that size however, I do not have explicit width and thickness dimensions.
Give this size, it is unlikely that it could have illuminated the entire temple by itself. However, I have seen reports that there were extra copies of the Menorah.
We have seen that Shlomo Hamelech had an additional ten copies of the menorah so that they may have been used to light the bais hamikdash and the second temple would have done something similar
The Holy Temple that King Solomon built was very similar to the Tabernacle (משכן) in its basic layout, albeit on a much larger scale. One very significant difference, however, was the fact that Solomon added an additional ten Menorot, as well as an additional ten Tables of the Showbread, which stood in the Kodesh Sanctuary. Altogether there were eleven Menorot and eleven Tables of the Showbread. The Menorot stood along the southern side of the Sanctuary and the Tables of the Showbread stood along the northern side. In the middle stood the golden Incense Altar.
Exodus 25:37 then adds, "And you shall make its lamps seven, and he shall kindle its lamps [so that they] shed light toward its face."
From this we learn that the seven lamps which held the oil and the wicks were separate from the Menorah.
This is further stated in Chronicles II, 4:20: "And the menorah and its lamps to kindle them as is required, before the Devir, (parochet separating the Sanctuary from the Holy of Holies), of refined gold." Again, the Menorah and the seven lamps are referred to as distinct and separate entities.
We see this distinction a third time in the words of the prophet Zechariah, 4:2: "And he said to me, "What do you see?" And I said, "I saw, and behold there was a menorah all of gold, with its oil-bowl on top of it, and its seven lamps thereon; seven tubes each to the lamps that were on top of it."
According to the Rambam, each of the seven lamps consisted of a bowl into which 1/2 log (approx. 285 grams) of pure olive oil was poured and the ptil (wick) was placed, and a cover to protect the oil and to keep it clean. It would be opened when cleaning out and replenishing the oil, as was done each morning, and closed before kindling the wick.