First I recommend you get Stephen Howards Haynes Saxophone manual.
Are there other symptoms - squeaks, difficult notes, octave jumps?
Leak lights are easy to make. You can find instructions on the web. However I made one from two super cheap D cell torches and a piece of bell wire. From one torch I took the lamp holder, trimmed the reflector until it would go down the sax neck, and connected the bell wire to it and refitted the bulb. . (I should have soldered it, but heat was going to melt the plastic, so I used tape). Make sure the wire comes straight(ish) out of the back of the holder, not at right abgles. The rest of the torch isn't needed. From the second torch I removed the 'lens' and connected the wire into the bulb holder where the bulb would normally go. Total cost - 2 euros, cos I had the bell wire in my tool box.
In a slightly darkened room, pass the light into the tube of the sax and look for light.... Any keys that should be open, close gently and see how the shut, should shut evenly all the way around, with very gentle finger pressure. Anything that needs firm pressure to close is leaking. Keys held shut by springs should be closed all round and need no extra pressure. Try opening and closing slowly. Should still seal evenly.
Make sure you look closely around the back of the pad as well. Often the keywork makes this difficult to see.
Watch also for keys closed by other keys. In an ideal world they close together. Often the don't and this leads to leaks. If you need significant pressure to get both key's closed, there's a leak.
You can also test with a cigarette paper, should be the same drag on the paper all the way round with almost no pressure on the key. Make sure you cut off the gummed part...
For octave pips, try pressing on the body octave key while you're playing - or get someone to help. For the neck pip, remove neck, block one end of the neck and blow in the other.
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