Days are Short etc Part 1

Let's explode a couple popular myths about immortals.

They are imposing physical specimens. 

Probably not. Go to a museum with a collection of armor. I stand about 5' 7" (170 cm) and first thing I noticed was I'd have a hard time squeezing into most of those suits. The exception was the suit of a king (I forgot who). That dude was at least 6' (183 cm) and must have been imposing as hell. So your immortal character might a petite person (immortal Neanderthals would be a bit shorter but much wider.) 

Does your immortality convey regeneration? If not your immortal might show the results of close calls, a missing eye or limb or just be scarred heavily. They might also be a complete mess and a total invalid... waiting for medicine to find a cure. Let's not even get into what gravity could do too a human body after centuries. Eek. 

They are filthy rich.

Assuming they work a few centuries and manage to bank some of it, it's reasonable to assume they are well off. In fact if they just kept throwing a bit of their money at different projects, sooner or later they would have to pick an IBM or Xerox. However, rich people do go broke. There are wars, depressions, hostile takeovers -not to mention throwing all your money into buggy whips, fountain pens, and eight track tapes. 

Savvy immortals will squirrel away funds over the years, just in case something like this happens. Then reaching their treasure is the problem. "Dear Sir or Madam, I am a thousand years old and recently fell on hard times. However, I distinctly remember where I cached some gold in East Africa. If you could help finance my recovery expedition I will gladly give you a third. I require..." Yes some players will answer that letter.

They were historical figures (some more than once).

Except, if immortals want to remain undiscovered, for whatever reason, they are not going to achieve fame or notoriety (infamy is another matter.) Having portraits all over, or your profile on coins will make it hard to start a new life when people notice you are not aging. This misconception is similar to the one where people access past lives, and invariably were someone famous. No one shoveled shit for a living in a past life.

The knowledge of the Ages and are highly skilled.

People have a finite memory like a flash drive. Sure, once you were a fantastic alchemist or chirurgeon or ostler but these professions were forgotten to allow you to remember the passcodes to your Swiss bank accounts, IT knowledge, and real estate legislature. Similarly, skills need to be practiced or lost. Swordplay? Guns are way easier. Screw tradition. A shotgun can take a guy's head off too. Alternately, your immortal may be hidebound and stubborn. They ride horses, don't drive, write letters, hate email and hang onto the stock in companies manufacturing buggy whips, fountain pens and eight track tapes (they're coming back I tell you!) Look for a handler then, a well paid mortal who protects them from themselves.

They are detached and aloof.

People band together to survive. Assuming immortality means an extended lifespan, without any regeneration, you will need other people to survive. People rarely put themselves out for sociopaths who do not value their underlings lives. They may get around this with really good wages and benefits but see my second point. Immortals may take decades to learn to charm, coax, seduce, and wheedle to get what they want but that is hardly aloof. They may be a weasel, but they are a charismatic weasel. A short, sometimes wealthy, sometimes scarred charming weasel.