The old timers are Ojitchi(Male) and Otokitchi(Female). Otokitchi normally appears as the matchmaker.
To get them, raise your Tamagotchi perfectly, and ignore the matchmaker, saying no every time she appears. They may evolve into Ojitchi or Otokitchi, depending on the gender.
This is confirmed working on the V1. I don't know how to get them on the V2 or V3, but the same tip may work.
I have had both of the old timers before. You can get them buy ignoring the matchmaker. When your tama is about 9 yeras old it will turn into an old timer. But if your tama is an old timer, the matchmaker will not come so it will pass away and you will have to start at gen 1 again.
For any Version of tamagotchi all you need to do is refuse the Matchmaker continuesly. She comes back alot of times. Keep in mind your tamagotchi will start over at generation 1 again.