Like Fortinet, F5's authentication interface is very Javascript-heavy.
Unlike with Fortinet, I didn't even both to try to parse and "follow" HTML forms.
For now, we just create a static form (with username and password fields),
ask the user to fill it out, submit it, and attempt to detect successful login
by a length-0 response including F5_ST and MRHSession cookies.
The F5_ST cookie appears to be a reliable(?) indicator of successful login.
It's a "session timeout" cookie (https://support.f5.com/csp/article/K15387),
which looks like '1z1z1z1612808487z604800'. The 4th field appears to be the
Unix epoch timestamp of session activation, and the 5th appears to be the
duration in seconds until it expires.