I am looking for an appendage to attach to the end of a telescope which splits the image into two eyes instead of one.
Does such an appendage exist?
Absolutely. You are looking for a binocular eyepiece, or a binocular viewer. Most of them require you to insert two matching ocular eyepieces, so it can be fairly expensive.
Most major telescope eyepiece manufacturers sell them. I'm not sure what the rules are for mentioning brand names, but a quick google for 'telescope binocular viewer' will turn up many examples.
You will require a decent telescope that can take standard 1.25" or 2" eyepieces. Also, the telescope needs a lot of 'back focus', which many Newtonian telescopes do not have. You may also need a barlow lens for focus, which will increase magnification but cut down the field of view and light gathering.
It would be best to check the specifications of the specific bino viewer and your telescope to see if they are compatible. If you have a Schmidt-Cassegrain scope, you should be fine and don't need the barlow.