I have a wood lathe with a #1 morse taper. Most of the accessories that I can get locally have an #2 taper. I need an adapter that will let me -for example- use a MT#2 pen mandrel in a MT#1 lathe. Is there such a thing in existence (or any other tool that I can use)? I've seen the opposite adapter being sold but for the life of me could not find the one I'm describing.
The thing you're looking for is called an extension socket. If you search for "Morse Taper Extension Socket MT1 to MT2" on Amazon you'll see several examples.
However, the best deal I found was from a seller on Etsy.
The #1MT is smaller than the #2MT, so essentially such a setup would be less safe than investing in the better equipment (a #2MT lathe). The "animal" would basically be a #1MT on one end, and a #2MT at the other end, leaving you hanging nearly 5 inches off your bearings before you even attach to your project.
In any case, any variance in concentricity would be multiplied and the effective wear on your bearings (not to mention the quality of the work) would be significant.
The reverse situation (#2MT to #1MT) has adapter sleeves (where the #1 sits inside the #2) you can use such as:
That said, there are many #1MT accessories at Penn State, Craft Supply, and Packard, if you look.
Someone mentioned a blacksmith, which may be an option, or a machine shop. Either could be more expensive than a new lathe that meets your needs.
Good luck with your search. I know getting started requires either creative thought or lots of money.