When I use Gmail to send an email, the email signature defined in the settings is automatically added at the bottom of the email. However, when I open a mailto link to send a message, the email signature is not automatically added.
Here's the code:
<a href="mailto:email@example.com?subject=Thanks for your time&body=Hi,%0A%0AIt%20was%20a%20real%20pleasure%20speaking%20with%20you.%20Thank%20you%20for%20your%20time%20and%20we'll%20be%20in%20touch%20soon." target="_blank">test</a>
Using body as a parameter in the mailto link replaces everything that is already placed into the email by Gmail. If body is not part of the attribute from mailto, then the signature works as expected.
Source: I tested this with your fiddle by removing the body attribute and clicked the link again. It works just as you want.
I have to add code to submit this answer with a fiddle, so here is the link that will work with a signature:
<a href="mailto:firstname.lastname@example.org?subject=Thanks for your time" target="_blank">test</a>