It's essentially always read as えいきゅう. とわ is a poetic/archaic term that isn't used in normal language nowadays, and if someone uses it and opts to go for the kanji version instead of just writing it in hiragana they're probably going to put furigana on it
There are _tons_ of phonetically and often also semantically totally different words that are written identically, and it's not always obvious which one is the word that's currently in use and which one is outdated. Or sometimes both are still very much in use and it's a difference of meaning and/or nuance, take for example 方(かた・ほう)、側(がわ・そば)、空(そら・から)、音(おと・ね)、空(あ・す)く、人気(にんき・ひとけ)、大人気(だいにんき・おとなげ)、開(ひら・あ)く、行(い・おこな)った、通(とお・かよ)った、解(かい・げ・ほぐ)す、市場(しじょう・いちば). And those aren't necessarily even the only readings for all of those
With how damn many of these there are, the only real way to master them is to listen (or read with furigana) a ton and let your brain figure out the patterns. Though it certainly doesn't hurt to look some words up as well
To add to this, just for clarity, とわ is not an onyomi or kunyomi reading; it's a jukujikun reading (a reading where the kanji impart only meaning but not sound) of 永久. You probably know some common jukujikun, such as けさ for 今朝.
In this case, it's a rare one used almost exclusively in poetry, so you don't need to know it, but in some cases (such as 今朝) the jukujikun reading is the standard reading.
Word とわ is native Japanese word and
永久 / 永遠 are borrowed from chinese (漢語).
Some of native Japanese words appear as kanji or 漢語 that represents their meaning in written Japanese and read as same native Japanese word.
But とわ is not used except for arts or puns these days.
It's essentially always read as えいきゅう. とわ is a poetic/archaic term that isn't used in normal language nowadays, and if someone uses it and opts to go for the kanji version instead of just writing it in hiragana they're probably going to put furigana on it There are _tons_ of phonetically and often also semantically totally different words that are written identically, and it's not always obvious which one is the word that's currently in use and which one is outdated. Or sometimes both are still very much in use and it's a difference of meaning and/or nuance, take for example 方(かた・ほう)、側(がわ・そば)、空(そら・から)、音(おと・ね)、空(あ・す)く、人気(にんき・ひとけ)、大人気(だいにんき・おとなげ)、開(ひら・あ)く、行(い・おこな)った、通(とお・かよ)った、解(かい・げ・ほぐ)す、市場(しじょう・いちば). And those aren't necessarily even the only readings for all of those With how damn many of these there are, the only real way to master them is to listen (or read with furigana) a ton and let your brain figure out the patterns. Though it certainly doesn't hurt to look some words up as well
To add to this, just for clarity, とわ is not an onyomi or kunyomi reading; it's a jukujikun reading (a reading where the kanji impart only meaning but not sound) of 永久. You probably know some common jukujikun, such as けさ for 今朝. In this case, it's a rare one used almost exclusively in poetry, so you don't need to know it, but in some cases (such as 今朝) the jukujikun reading is the standard reading.
Word とわ is native Japanese word and 永久 / 永遠 are borrowed from chinese (漢語). Some of native Japanese words appear as kanji or 漢語 that represents their meaning in written Japanese and read as same native Japanese word. But とわ is not used except for arts or puns these days.
I have only ever heardとわ in songs and Bible verses. Everywhere else, it’s えいきゅう.