How can I move my signature from one Mac Mail account to another?
It seems like you are trying to do two different things a) attach an image to a signature; b) assign a signature to an account.

To attach an image to your signature.


After you open the Apple Mail preferences click on the Signature tab.
In the left column click on 'All Signatures'.
Either click on an existing signature, or click on the '+' button below the middle column. Then select your new signature.
In the right column, after editing your signature, place the cursor where you would like the image to appear.
Open Finder and navigate to the location of the image you would like to ado your signature.
Left-click and hold, then drag the image file to the signature panel. Then release the mouse button.


You should now see the image in your signature.

To assign a signature to an account.


After you open the Apple Mail preferences click on the Signature tab.
In the left column click on 'All Signatures'.
Click in the middle column.
Left-click and hold on the signature you want to associate with the new account.
Drag the signature to the new account and release the mouse button.


FYI, if you have multiple signature assigned to an account, you can change the order in which the signatures automatically appear by drawing them in said order. Then from the “Choose Signature” pop-up menu, below the signatures panel, select “In Sequential Order”.