Why wont the eclipse tattoo thermal copier transfer the image to the thermal paper even when the paper is put in correctly?

If your using the 'eclipse' that is a fax machine and does not produce enough heat, this is why the copy does not come through. A fax header is low voltage and low heat - it can't get through all the layers of the tattoo paper.

There is an 'ECLIPSE 2' version which is a true thermal-copier and uses an IR heat lamp and does work.

You need to use a carrier with this type of machine, not just putting the paper in on it's own like the 'eclipse' model it sounds like you have.