I'm not a teacher. Just speaking as a native speaker, I doubt that there is any <em>useful</em> rule or explanation.

It is pronounced one way in <em>bringer, clinger, pinger, singer, winger, zinger. </em>

It is pronounced another way in <em>finger </em>and<em> linger.</em>

And, of course, a third way, like a <em>j</em>, in <em>binger </em>(one who binges) and <em>ginger.</em>

As a practical matter, English just isn't spelled phonetically. I think of letters in English as just memory aids, that <em>help</em> us remember the the sound of the word. In US schools English is taught through a mixture of two techniques: phonics (looking at individual letters), and sight recognition (learning a word as a unit from the total appearance of the whole word). We are rarely taught spelling or pronunciation rules. When in doubt, we don't try to remember rules, we check a dictionary and memorize what the dictionary tells us.

People often know words from reading but do not hear them spoken for decades. It is quite common to hear a native speaker say "Oh, really, is it pronounced <em>that</em> way? I've been saying it wrong all my life." I won an argument with my English teacher in tenth grade about the pronunciation of the word "pagination." (He thought the first syllable was pronounced like "page," but it is pronounced to rhyme with "badge.")

Som Bhatta is right. It's all to do with morphology - how the building blocks of meaning fit together.

First, I'll correct two misconceptions in your question. The 'g' is not a syllable: it's a sound. Syllables have to contain vowels, so both these words are made up only two syllables. Also, the 'g' has not disappeared - it has never been there.

Now for the morphology. The words 'finger' and 'singer' look the same, but their morphology is different. While 'finger' is one indivisible unit, 'singer' is two - the base word 'sing' and the suffix 'er'. The base word is pronounced /sɪŋ/, and this does not change whern the verb is made into a noun with the 'er' suffix, /sɪŋər/, or when it becomes a participle,'singing' /sɪŋiɪŋ/.

Now a couple of things to confuse the issue:

One exception to this rule is with comparatives and superlatives. When we add comparative and superlative suffixes to adjectives, the 'g' is added. This is why the comparative adjective 'longer' is has a /ŋg/ in the middle, but the present participle and noun 'longing' only has a /ŋ/.

There are regional variations. If you happen to meet someone who comes from the West Midlands or North West of England, you might notice that they always pronounce /ŋg/ in the middle of words, even 'singer' and 'longing'. Even people who move away from these areas and acquire other accents still often retain this regional quirk.

So far as I know, singer comes from the word sing, so it retains that sound. However finger doesn't come from fing, so the g is pronounced. A native speaker or better still a native teacher may have a better explanation.

I think you mean signer not singer. Finger and singer both have the "g" sound. In signer the "g" is silent. "G" before an "n" is silent, like a "k" before an "n".

I believe, all you have to get here is to look how people say it, your audio memory, and a bit of imagination. That reminds me a story about the reading of Japanese names.

There was a man, had been summoned to appear before a jury. On the paper his name was shown by one single character with a simple meaning of "one". But that character has at leas 7 not so simple different readings.

So,now - Mr. Ichi! - no coming, - Mr. Hitotsu! - no coming, - Mr Itsuwa! - none - Mr. Itsuni! - neither - Mr. Itsuno! - silence.

A chairman wipes drops of sweat from his forehead and utters his last desperate cry - Mr. Hazime! (= "a start" or " the beginning"). - Hai! - the needed man stands up.

I also knew a real man whose name was Hitachi (you can make it out that it has to be written in two characters "a sun" + "coming out", like a company), but the real characters were "Tsuki"+"De" ("the moon" + "getting out").