->submit_form would be the proper way if there was a submit element in the form. This is obviously not the case for your project.

It may be inconvenient, but when automating a website, there is very little to no way around also learning/knowing a bit of HTML and Javascript. The <a class="chase-button ... element is a link, which you have to click after filling out the form. Most likely, that link then triggers some Javascript which collects the values previously filled into that form and sends them to the server.

If the call to ->follow_link(url => ... fails, then most likely, there is no such link. You will have to inspect the HTML closer. At least from the HTML snippet you posted, the link you want to click has no href attribute. It is contained in a <div> element with the class name loginBtn. I would try first clicking on that div, and if that doesn't work, clicking on the link. The <div> can be found by something like:

my $target= $mech->selector('.loginBtn', single => 1 );
[download]

The link could be found by something like:

my $target= $mech->selector('.loginBtn a', single => 1 );
[download]