Recover 8 year old Gamertag from Xbox 360?

Yes you can. Since you're able to sign into it to see that page, you can just sign into the same account on the console.

[quote user="DarkhavenX666"]

So if I have a VERY old Xbox gamertag from circa 2002 (Darkhaven3) which I have never used on Xbox 360, would I be able to change my current Gamertag (as in, legitimately buy a change for 800M$P) to this old tag?

[/quote]

No. You cannot join Xbox LIVE Gamertags. Unless recovered that gamertag with the Windows Email details to Xbox LIVE and
then paid the 800 Microsoft Points to change the 2002 Gamertag to something else, and then paid another 800 Microsoft Points ot change your current gamertag to the old one.

But all that would achieve would just be changing your gamertag to your old gamertag and that is all. Nothing else would be transfered from your 2002 Gamertag to your 2012 Gamertag, like Xbox LIVE Tenture (number of years on Xbox LIVE). That would all remain
on the recovered 2002 Gamertag.

Comment....

I Still use my Xbox from time to time. The 360 is about 8 years old now, The Xbox is a bit older

[quote user="Gamer Nostalgia"]
Your gamertag is 12 years old yet your oldest achievement is only from 2005..

[/quote] My gamertag is also 12 years old, and I can inform you that there were no achievements on the xbox, they started on xbox 360.

Check this link to locate the email:
https://support.xbox.com/en-US/my-account/microsoft-account/forgot-microsoft-account-solution