At first glance this looks like a duplicate of Gmail signature not working on mailto, but it isn't: In that other question, the problem was due to the mailto link specifying a "body" attribute, so gmail uses that as the body, instead of the usual blank-with-a-signature default body. That seems reasonable, as a behaviour.
In my case (and others I've tested it with), clicking on any mailto link (including ones that just have the email address, and no other attributes) will open a new email in Gmail, but the email will not have the signature.
Is this a known bug with Gmail? I'm using Version 67.0.3396.79 (Official Build) (64-bit)
EDIT: Yes, it's a known bug. See comments below.